Pith. sign in

REVIEW 3 major objections 4 minor 300 references

Linear and nonlinear supersymmetry in field and string theory

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This thesis argues that consistent effective theories of nonlinear supersymmetry must be built from constraints that remove only physical fields, not auxiliary fields, and uses that rule to derive improved supergravity models, a unique…

desk verdict A careful, honest thesis with four genuinely new results; the headline criterion of Chapter 1 is well argued but rests on an inference, not a theorem, so the universality claim should be read with that caveat. read the letter →

arxiv 2506.20396 v2 pith:CFFFKOEE submitted 2025-06-25 hep-th hep-ph

Gabriele Casagrande This is my paper
classification hep-thhep-ph
keywords constrainedsuperfieldsnonlinearsupersymmetrygoldstinosupergravitymassivegravitinospin-2orientifoldS-duality
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This thesis tries to establish a consistency criterion for effective theories with nonlinearly realized supersymmetry: constrained superfields—superfields with extra algebraic conditions that remove components to mimic the decoupling of heavy superpartners—are trustworthy only when the constraint removes physical fields and leaves auxiliary fields alone. It argues that the orthogonal constraint and the complex-scalar constraint fix auxiliary fields, force higher-derivative interactions into the ultraviolet theory, and make the speed of goldstino perturbations exceed light speed unless extra inequalities hold over all field space; the improved constraints it writes down remove the same fields without touching auxiliaries and are causal everywhere. It then uses this framework in supergravity to revisit gravitational production of massive gravitinos, claiming that the standard instantaneous-Hamiltonian Fock space does not match the stress-energy-tensor Fock space, with a mismatch that persists at high momenta. A further result is that the leading-order coupling of the massive spin-2 supermultiplet to four-dimensional $N=1$ supergravity, built from the supercurrent superfield, is unique and differs from the Kaluza-Klein coupling, with a higher strong-coupling scale. The string-theory part proposes a non-supersymmetric Scherk-Schwarz orientifold of type IIB whose O-planes couple only to twisted-sector states and which is conjectured to be S-duality invariant.

What carries the argument

The load-bearing object is the nilpotent goldstino superfield $S$ with $S^2 = 0$, together with the generalized single-component constraint $\bar S S Q_L = 0$, which can remove one component of another superfield at a time. The thesis shows that the orthogonal constraint decomposes into three such conditions—removing the imaginary scalar, the fermion, and the auxiliary field—and that dropping only the auxiliary-field condition yields a causal theory with the same minimal spectrum. In the supergravity chapters the carrying devices are the supercurrent superfield (the superspace multiplet containing the supersymmetry current and the stress-energy tensor) for building the unique massive spin-2 coupling, and the Bogolyubov transformation (a change of basis between two Fock spaces) for comparing instantaneous-Hamiltonian and stress-energy-tensor notions of particles in an FLRW background. The string-theory construction is carried by a twisted Scherk-Schwarz orientifold projection in which O-planes couple only to twisted-sector states.

What would settle it

Find an explicit ordinary two-derivative ultraviolet model whose low-energy limit reproduces the orthogonal-constraint goldstino lagrangian with a faster-than-light sound speed on some time-dependent background; if such a completion exists, the claim that superluminality signals the absence of a standard completion is false.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a diagnostic for constrained superfields: a constraint that fixes an auxiliary field—rather than a physical scalar or fermion—cannot define a consistent low-energy theory of nonlinear supersymmetry, because an auxiliary field has no mass threshold to decouple and its removal puts higher-derivative operators directly in the ultraviolet. Applied to the orthogonal constraint (1.4.6) and the complex-scalar constraint (1.4.24), this yields goldstino sound speeds whose squares exceed one unless the field-space inequalities (1.4.22) and (1.4.32) hold, and those inequalities are in tension with the positivity bounds on the $2\to 2$ amplitudes. The improved constraints (1.4.43) remove the same physical components while leaving the auxiliary field $F_\phi$ untouched, and their sound speed (1.4.51) is subluminal everywhere. The thesis extends the same criterion to supergravity, where the longitudinal gravitino sound speed matches the rigid goldstino speed; it separately claims a unique leading-order coupling of the massive spin-2 supermultiplet to new-minimal supergravity, with higher-derivative non-minimal terms and a $\Lambda_4$ cutoff, distinct from the Kaluza-Klein coupling; and it constructs a twisted Scherk-Schwarz orientifold with fully broken supersymmetry whose S-duality is conjectured.

Load-bearing premise

The load-bearing premise is that a low-energy warning sign—a sound speed above light speed or a positivity condition that fails—definitively proves the model cannot come from an ordinary two-derivative ultraviolet theory, and the thesis presents this as an argued criterion rather than a proven theorem.

Editorial extensions

If this is right

  • Minimal supergravity models of inflation built on the orthogonal constraint are consistent only when $h(A)|f(A)|^2 \geq 2|g'(A)|^2$ across all field space; the improved constraints keep the same minimal field content without that inequality.
  • Gravitational gravitino production should be computed from the stress-energy tensor Fock space rather than the instantaneous-Hamiltonian one, since the two disagree for the longitudinal gravitino even in the high-momentum limit.
  • The unique leading-order coupling of the massive spin-2 supermultiplet to new-minimal supergravity involves higher-derivative non-minimal metric and gravitino terms and raises the strong-coupling scale from $\Lambda_5$ to $\Lambda_4$.
  • The twisted Scherk-Schwarz orientifold provides a non-supersymmetric type IIB vacuum with O-planes coupling only to twisted-sector states, conjecturally S-duality invariant and describable in F-theory.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the physical-versus-auxiliary test could be applied to any constrained superfield model in the literature, flagging constraints whose solutions force nonlinear goldstino dependence into auxiliary fields as the first place to look for hidden faster-than-light propagation.
  • Editorial inference: the gravitino Fock-space mismatch suggests that cosmological production rates and derived limits based on the vanishing-sound-speed divergence should be recomputed with the stress-energy tensor before being used as constraints on supergravity cosmology.
  • Editorial inference: the uniqueness of the massive spin-2 supercurrent coupling could be probed by computing gravitino-mediated $2\to2$ amplitudes; a different cutoff or pole structure would indicate that additional consistent couplings exist beyond the one the supercurrent argument finds.
  • Editorial inference: the conjectured S-duality of the twisted orientifold could be tested by computing the one-loop vacuum amplitude in both duality frames; agreement would show that string dualities can survive complete supersymmetry breaking.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This PhD thesis, based on the author's papers [1]–[4], studies effective field theories with nonlinearly realized supersymmetry, the cosmological dynamics of massive gravitinos, the leading-order coupling of a massive spin-2 multiplet to supergravity, and a new non-supersymmetric Scherk–Schwarz orientifold of type IIB string theory. Chapter 1 derives the lagrangians and sound speeds for constrained-superfield models, argues that constraints which fix auxiliary fields are inconsistent with a two-derivative UV completion, and proposes improved constraints with the same physical spectrum. Chapter 2 revisits gravitational particle production, shows that the instantaneous Hamiltonian and the stress-energy tensor define different Fock spaces for the longitudinal gravitino, and constructs a unique coupling of the massive spin-2 multiplet to new-minimal supergravity. Chapter 3 constructs a twisted orientifold with O-planes coupling only to the twisted sector, conjectures S-duality and an F-theory description, and analyzes the D-brane spectrum.

Significance. If the Chapter 1 criterion is correct, it is a useful diagnostic for constrained-superfield models and it has already led to improved supergravity inflation models; the Chapter 2 gravitino analysis exposes a subtlety in gravitational particle production that deserves further study; the unique spin-2 coupling in Chapter 2 is a concrete, calculable result with implications for the string lamppost principle; and the Chapter 3 construction provides a new non-supersymmetric string vacuum. The thesis is unusually detailed and careful: the derivations are explicit, the rigid-limit sound speeds are cross-checked against the supergravity results through the equivalence theorem, and the D-brane spectra are computed in detail. The main weakness is that the headline criterion of Chapter 1 is presented as established while the body of the text itself labels the key step as an argument, not a proof; the condition is therefore a well-supported conjecture rather than a theorem.

major comments (3)
  1. [§1.4.1, §1.4.3; Eqs. (1.4.17)–(1.4.22)] The paper's central criterion is presented as established—the abstract says 'we establish a criterion' and §1.4.3 says consistent effective field theories 'must' be constructed through constraints that remove only physical degrees of freedom—but the derivation relies on a step that the text itself labels as an argument: 'we argue in [1] that the vacuum positivity bound (1.4.19) must nevertheless be extended to the whole functions domain.' The inference from a superluminal sound speed on a time-dependent background, or from violation of field-space-extended positivity bounds, to the absence of any standard two-derivative UV completion is an assumption of the EFT positivity programme, not a proven theorem. If this inference fails, the orthogonal and complex-scalar constraints are not 'inconsistent' but merely superluminal in parts of field space, and the improved constraints of §1.4.3 are one repair rather than the uniquely mandated construction. Please either supply a proof of the necessity claim, or reformulate the abstract and §1.4.3 so that the criterion is explicitly stated as a conjecture supported by the two worked examples.
  2. [§1.4.3; Eqs. (1.4.8), (1.4.40)–(1.4.42)] The claim that a superfield constraint fixing an auxiliary field 'requires higher-derivative operators already in the UV' is not demonstrated in the manuscript. The orthogonal-constraint example shows that the solution for the auxiliary F_phi in eq. (1.4.8) contains derivatives of A and G, but algebraic elimination of an auxiliary field in a derivative-coupled theory can produce such derivative expressions without changing the operator content of the UV action. The thesis also does not exhibit an explicit two-derivative UV completion of the improved models; it infers their existence from the absence of a constrained auxiliary. To make the central conclusion load-bearing, please derive the implication for the UV operator content, or explicitly restrict the claim to constraints of the form (1.4.38)–(1.4.42) and present the improved models as a consistency repair rather than as the unique allowed construction.
  3. [§2.2.3–2.2.4; Eqs. (2.2.100), (2.2.112)–(2.2.115)] The central gravitino result—that the physical energy operator is the one computed from (2.2.100), that it removes the cs→0 divergence, and that its Fock space does not coincide with the instantaneous-Hamiltonian Fock space even in the UV (2.2.115)—depends on a particular choice of stress-energy tensor. The gravitino stress-energy tensor is defined only up to identically conserved improvement terms, and different supercurrent improvements are known to shift T^{mu nu}. Please show that the UV limit (2.2.115), the finite part of the Bogolyubov coefficients (2.2.114), and the statement that 'the energy of the longitudinal gravitino is not associated with any divergence' are invariant under such improvements and under the canonical rescaling (2.2.14). Without this check, the 'physical' status of the proposed energy operator is not fully established.
minor comments (4)
  1. [§2.2.1, Eq. (2.2.35)] The causality constraint in (2.2.35) has the inequality reversed: c_s^2 ≤ 1 from (2.2.34) requires f(phi)^2 ≥ 2 g'(phi)^2, not ≤, in agreement with the rigid-limit condition (1.4.22). Please correct this sign.
  2. [§2.2.4] The sentence 'The issue disappears once the improved setup of eq. (1.4.3) proposed in [1] is employed' should refer to eq. (1.4.43), not eq. (1.4.3), which is the Volkov–Akulov lagrangian.
  3. [§1.2.1] There are several typographical errors in the Kähler geometry paragraph, including 'K¨haler-geometrical' and inconsistent umlauts. A careful proofreading pass over the whole manuscript is needed.
  4. [§3.4 and Abstract] The S-duality invariance and F-theory formulation of the new orientifold are conjectural statements ('we argue'), but the abstract and chapter summary do not consistently separate these conjectures from the derived D-brane spectrum and vacuum-energy results. Please add an explicit statement in the summary of Chapter 3 distinguishing proven results from conjectures.

Circularity Check

1 steps flagged · score 2.0 of 10

Chapter 1's 'remove only physical, not auxiliary, degrees of freedom' criterion is mutually defined with the improved constraints (1.4.43) used to validate it; the superluminality-to-no-UV-completion step is a labeled argument within the thesis, so the criterion is argued rather than forced.

  1. self definitional [§1.4.3, eqs. (1.4.40)-(1.4.43), (1.4.47)-(1.4.51)]
    "following the previous discussion about ill-defined goldstino couplings and constraints on the auxiliary fields, the decomposition above suggest considering the effective theory generated only by the first two constraints (1.4.40)-(1.4.41) ... without the third one (1.4.42): the resulting model will be an improved version of the orthogonal constraint (1.4.6), with the same minimal field spectrum but without touching the auxiliary field [1]. ..."

    The stated criterion is the design principle used to select the improved constraints (1.4.43): the thesis deletes from the orthogonal constraint precisely its auxiliary-field-fixing member (1.4.42), then invokes the improved model's 'subluminal at all times' sound speed as 'the strongest evidence supporting the claim on constrained auxiliary fields.' The criterion and the construction are mutually defined: the criterion says only constraints that avoid auxiliary fields are consistent; the improved constraints are built to avoid auxiliary fields; and their causality is then presented as proof of the criterion.

full rationale

This thesis reproduces its four source papers [1]-[4] with the load-bearing derivations in the text: the goldstino sound speeds (1.4.21), (1.4.31), (1.4.51), the 2→2 amplitudes (1.4.17)-(1.4.18), the gravitino stress-energy tensor (2.2.100) and Bogolyubov analysis (2.2.112)-(2.2.115), the supercurrent classification of §2.4, and the orientifold/D-brane spectrum of §3.4. These are parameter-free derivations with stated assumptions and external cross-checks (agreement with the literature's supergravity sound speeds [69,70,77]; equivalence-theorem alignment of (2.2.117)-(2.2.119); the dRGT/Λ3 cutoff lore), so the heavy self-citation does not by itself raise the circularity score. The Chapter 1 criterion rests on an inference the thesis itself labels as argued: 'we argue in [1] that the vacuum positivity bound (1.4.19) must nevertheless be extended to the whole functions domain' (§1.4.1), and 'we interpret this as an obstruction to a completion into a microscopic 2-derivative theory.' If that inference fails, the constrained models are merely superluminal on some backgrounds, and the improved models are one repair rather than the uniquely mandated construction; this is a correctness and robustness risk, not a circular step, and the thesis's honest hedging keeps the score low. The uniqueness claim of §2.4.2 is derived within the thesis via the supercurrent formalism with the amplitude computation of §2.4.4 and the Kaluza-Klein comparison of Appendix C, and the S-duality claim of §3.4 is explicitly a conjecture. The only mild self-referential loop is the one flagged in the steps. Overall, this is a self-contained work with no significant circularity.

Assumptions & free parameters 2 free parameters · 6 assumptions · 1 invented entities

The central claims rest on standard superspace, supergravity and string-theory background (counted as standard math), plus three paper-specific premises: (i) the auxiliary-field and higher-derivative link imported from [61] and the field-space extension of positivity bounds, on which the 'inconsistency' criterion leans; (ii) the identification of the physical gravitino energy with the stress-energy tensor, on which the gravitino chapter's puzzle is built; (iii) the conjectured S-duality of the new orientifold. The only hand-chosen inputs are the model functions (superpotentials and Kähler potentials) that define the EFTs; no constants are fitted to data anywhere. These premises are flagged in the text as arguments or conjectures rather than hidden, which limits circularity but does not remove the burden.

free parameters (2)
  • Superpotential and Kähler functions f(Φ), g(Φ), h(A), κ(Φ,Φ̄) = unspecified functions, chosen by hand
    These define the model space of the constrained-superfield EFTs (eqs. (1.4.9), (1.4.26), (1.4.46)) and in §2.2 engineer the inflationary potential V(φ) = f² − 3g². They are model inputs, not fitted to data; the causality bounds (1.4.22) and (1.4.32) are inequalities they must satisfy.
  • Scherk-Schwarz deformation twist of the new orientifold = not specified numerically
    The §3.4 construction is a Scherk-Schwarz deformation in nine dimensions; the twisting is the geometric input that breaks supersymmetry and sets the O-plane couplings to the twisted sector. It is chosen by hand within a standard class of string compactifications, not fitted to any external datum.
assumptions (6)
  • standard math Standard N=1 rigid and local supersymmetry background: superspace formalism, superfield constraints, Kähler geometry, the super-Higgs mechanism and the gravitino equivalence theorem.
    Invoked throughout Chapters 1 and 2 (e.g., §1.2, §2.1.2) as the accepted framework within which the original results are derived.
  • domain assumption The generalized-constraint result of [61]: a constraint of the form (1.4.38) can remove single superfield components, and a constraint that fixes an auxiliary field is a higher-derivative operator in the UV.
    This is the load-bearing premise of the inconsistency criterion in §1.4.3; it is cited from prior literature, not proven in the thesis.
  • domain assumption Positivity bounds apply to the goldstino and scalar 2-to-2 amplitudes (eqs. (1.4.17)-(1.4.19)), and the vacuum bound extends to the whole field space, giving subluminality conditions (1.4.22) and (1.4.32).
    The thesis 'argues' this extension in §1.4.1-1.4.2; the criterion stands or falls on whether IR superluminality implies absence of a two-derivative UV completion.
  • domain assumption The physical energy of the longitudinal gravitino is given by the on-shell stress-energy tensor (2.2.100), so the instantaneous-Hamiltonian Fock space is not the physical one.
    Section 2.2.3: the central claim of the gravitino chapter, the UV misalignment (2.2.115), follows from this identification, whose origin the authors state they do not understand.
  • domain assumption Every consistent leading-order coupling of a rigid multiplet to D=4 N=1 supergravity is captured by a supercurrent superfield of the type in §2.3.
    Section 2.4: the uniqueness theorem ('only a single class of such couplings') is derived inside the supercurrent formalism; the completeness of that formalism converts 'one coupling found' into 'only one coupling exists'.
  • domain assumption The new Scherk-Schwarz orientifold is invariant under S-duality and admits an F-theory formulation.
    Abstract and §3.4.1: stated as an argued conjecture; the vacuum energy and D-brane spectrum in §3.4.2-3.4.3 are computed under this assumption.
invented entities (1)
  • Twisted orientifold planes (O-planes coupling only to the twisted sector of the Scherk-Schwarz orbifold)
    purpose: Realize complete supersymmetry breaking in the new type IIB orientifold, with S-duality acting nontrivially; central to the §3.4 construction.
    The construction is self-consistent (tadpole analysis, D-brane spectrum, vacuum energy in §3.4.2-3.4.3), but there is no experimental or independent worldsheet handle outside the model; it generalizes the previously known 6D twisted O-planes reviewed in §3.3.4.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Linear and nonlinear supersymmetry in field and string theory." pith.science (2026). https://pith.science/paper/CFFFKOEE

@misc{pith2026250620396,
  author       = {Pith},
  title        = {Pith review of: Linear and nonlinear supersymmetry in field and string theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CFFFKOEE}},
  note         = {Machine review of arXiv:2506.20396}
}
read the original abstract

This Ph.D. thesis investigates effective field and string theories in which supersymmetry is realized and broken in various ways. Chapter 1 addresses effective theories with nonlinearly realized supersymmetry, constructed using the formalism of constrained superfields. We establish a criterion for identifying inconsistent constraints, formulate their improved versions, and propose, along these lines, improved supergravity models of inflation. In Chapter 2, we discuss a peculiar application of this framework: the gravitational production of massive gravitinos in time-dependent backgrounds. We emphasize some physical subtleties in the standard description of this mechanism, which become particularly severe in the case of the gravitino. Next, the focus shifts to linear supersymmetry, and we investigate the leading-order coupling of the massive spin-2 field supermultiplet to pure supergravity in four dimensions. This analysis is carried out using the supercurrent superfield formalism, and it shows that only a single class of such couplings can be consistently defined. This is fundamentally distinct from the coupling obtained by compactifying higher-dimensional supergravities, and it has interesting connections to string theory and the string lamppost principle. Finally, in Chapter 3, we present a novel orientifold projection of type IIB string theory. This is a Scherk--Schwarz orientifold in which supersymmetry is entirely broken, and the O-planes couple only to the twisted sector of the theory. We argue that this model is invariant under S-duality and can be formulated as an F-theory compactification. We also analyze the D-brane spectrum of the theory and compare the results with earlier similar constructions. All original findings presented in this thesis are preceded by a comprehensive and detailed introduction to the general frameworks to which they belong.

Figures

Figures reproduced from arXiv: 2506.20396 by the authors.

Figure 1.1
Figure 1.1. Basic representation of supersymmetry preserving versus supersymmetry breaking vacua. [PITH_FULL_IMAGE:figures/full_fig_p035_1_1.png] view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

300 extracted references · 28 canonical work pages

  1. [1]

    Bonnefoy, G

    Q. Bonnefoy, G. Casagrande and E. Dudas,Causality constraints on nonlinear supersymmetry, JHEP 11 (2022) 113, [2206.13451]

    arXiv 2022

  2. [4]

    Bossard, G

    G. Bossard, G. Casagrande, E. Dudas and A. Loty,A unique coupling of the massive spin-2 field to supergravity, 2502.09599

    arXiv

  3. [2]

    Casagrande, E

    G. Casagrande, E. Dudas and M. Peloso,On energy and particle production in cosmology: the particular case of the gravitino, JHEP 06 (2024) 003, [2310.14964]

    arXiv 2024

  4. [3]

    Bossard, G

    G. Bossard, G. Casagrande and E. Dudas,Twisted orientifold planes and S-duality without supersymmetry, JHEP 02 (2025) 062, [2411.00955]

    arXiv 2025

  5. [5]

    S. L. Glashow,Partial Symmetries of Weak Interactions, Nucl. Phys.22 (1961) 579–588

    1961

  6. [6]

    Weinberg,A Model of Leptons, Phys

    S. Weinberg,A Model of Leptons, Phys. Rev. Lett.19 (1967) 1264–1266

    1967

  7. [7]

    Salam,Weak and Electromagnetic Interactions, Conf

    A. Salam,Weak and Electromagnetic Interactions, Conf. Proc. C680519 (1968) 367–377

    1968

  8. [8]

    Englert and R

    F. Englert and R. Brout,Broken Symmetry and the Mass of Gauge Vector Mesons, Phys. Rev. Lett.13 (1964) 321–323

    1964

Show all 300 references
  1. [9]

    P. W. Higgs,Broken Symmetries and the Masses of Gauge Bosons, Phys. Rev. Lett. 13 (1964) 508–509

    1964

  2. [10]

    Aad et al.,Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys

    ATLAScollaboration, G. Aad et al.,Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1–29, [1207.7214]

    2012 arXiv

  3. [11]

    Chatrchyan et al.,Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys

    CMS collaboration, S. Chatrchyan et al.,Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett. B716 (2012) 30–61, [1207.7235]

    2012 arXiv

  4. [12]

    Aoyama, M

    T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio,Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant, Phys. Rev. Lett.109 (2012) 111807, [1205.5368]

    2012 arXiv

  5. [13]

    X. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse,Measurement of the Electron Magnetic Moment, Phys. Rev. Lett.130 (2023) 071801, [2209.13084]

    2023 arXiv

  6. [14]

    Muon g-2 collaboration, G. W. Bennett et al.,Measurement of the negative muon anomalous magnetic moment to 0.7 ppm, Phys. Rev. Lett.92 (2004) 161802, [hep-ex/0401008]

    2004 arXiv

  7. [15]

    M. H. Goroff and A. Sagnotti,QUANTUM GRAVITY AT TWO LOOPS, Phys. Lett. B 160 (1985) 81–86

    1985

  8. [16]

    M. H. Goroff and A. Sagnotti,The Ultraviolet Behavior of Einstein Gravity, Nucl. Phys. B266 (1986) 709–736

    1986

  9. [17]

    Veneziano,Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cim

    G. Veneziano,Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cim. A57 (1968) 190–197

    1968

  10. [18]

    M. A. Virasoro,Alternative constructions of crossing-symmetric amplitudes with regge behavior, Phys. Rev.177 (1969) 2309–2311

    1969

  11. [19]

    J. A. Shapiro,Narrow-resonance model with regge behavior for pi pi scattering, Phys. 165 Rev.179 (1969) 1345–1353

    1969

  12. [20]

    Scherk and J

    J. Scherk and J. H. Schwarz,Dual Models for Nonhadrons, Nucl. Phys. B81 (1974) 118–144

    1974

  13. [21]

    Yoneya,Connection of Dual Models to Electrodynamics and Gravidynamics, Prog

    T. Yoneya,Connection of Dual Models to Electrodynamics and Gravidynamics, Prog. Theor. Phys.51 (1974) 1907–1920

    1974

  14. [22]

    M. B. Green and J. H. Schwarz,Supersymmetrical String Theories, Phys. Lett. B109 (1982) 444–448

    1982

  15. [23]

    D. J. Gross, J. A. Harvey, E. J. Martinec and R. Rohm,The Heterotic String, Phys. Rev. Lett.54 (1985) 502–505

    1985

  16. [24]

    Witten,String theory dynamics in various dimensions, Nucl

    E. Witten,String theory dynamics in various dimensions, Nucl. Phys. B443 (1995) 85–126, [hep-th/9503124]

    1995 arXiv

  17. [25]

    Candelas, G

    P. Candelas, G. T. Horowitz, A. Strominger and E. Witten,Vacuum configurations for superstrings, Nucl. Phys. B258 (1985) 46–74

    1985

  18. [26]

    M. R. Douglas,The Statistics of string / M theory vacua, JHEP 05 (2003) 046, [hep-th/0303194]

    2003 arXiv

  19. [27]

    Wess and B

    J. Wess and B. Zumino,A Lagrangian Model Invariant Under Supergauge Transformations, Phys. Lett. B49 (1974) 52

    1974

  20. [28]

    Wess and B

    J. Wess and B. Zumino,Supergauge Transformations in Four-Dimensions, Nucl. Phys. B 70 (1974) 39–50

    1974

  21. [29]

    S. R. Coleman and J. Mandula,All Possible Symmetries of the S Matrix, Phys. Rev. 159 (1967) 1251–1256

    1967

  22. [30]

    R. Haag, J. T. Lopuszanski and M. Sohnius,All Possible Generators of Supersymmetries of the s Matrix, Nucl. Phys. B88 (1975) 257

    1975

  23. [31]

    D. Z. Freedman, P. van Nieuwenhuizen and S. Ferrara,Progress Toward a Theory of Supergravity, Phys. Rev. D13 (1976) 3214–3218

    1976

  24. [32]

    Deser and B

    S. Deser and B. Zumino,Consistent Supergravity, Phys. Lett. B62 (1976) 335

    1976

  25. [33]

    Z. Bern, L. J. Dixon and R. Roiban,Is N = 8 supergravity ultraviolet finite?, Phys. Lett. B644 (2007) 265–271, [hep-th/0611086]

    2007 arXiv

  26. [34]

    Wess and J

    J. Wess and J. Bagger,Supersymmetry and supergravity. Princeton University Press, Princeton, NJ, USA, 1992

    1992

  27. [35]

    Bertolini,Supersymmetry - From the basics to exact results in gauge theories

    M. Bertolini,Supersymmetry - From the basics to exact results in gauge theories. World Scientific, 12, 2024, 10.1142/14026

    2024 doi

  28. [36]

    Bilal,Introduction to supersymmetry, hep-th/0101055

    A. Bilal,Introduction to supersymmetry, hep-th/0101055

    arXiv

  29. [37]

    S. P. Martin,A Supersymmetry primer, Adv. Ser. Direct. High Energy Phys.18 (1998) 1–98, [hep-ph/9709356]

    1998 arXiv

  30. [38]

    S. J. Gates, M. T. Grisaru, M. Rocek and W. Siegel,Superspace Or One Thousand and One Lessons in Supersymmetry, vol. 58 ofFrontiers in Physics. 1983

    1983

  31. [39]

    D. Z. Freedman and A. Van Proeyen,Supergravity. Cambridge Univ. Press, Cambridge, UK, 5, 2012, 10.1017/CBO9781139026833

    2012 doi

  32. [40]

    Dall’Agata and M

    G. Dall’Agata and M. Zagermann,Supergravity: From First Principles to Modern Applications, vol. 991 ofLecture Notes in Physics. 7, 2021, 10.1007/978-3-662-63980-1

    2021 doi

  33. [41]

    Antoniadis, E

    I. Antoniadis, E. Dudas, F. Farakos and A. Sagnotti,Non-Linear Supergravity and Inflationary Cosmology. 9, 2024. 2409.14943

    2024 arXiv

  34. [42]

    Salam and J

    A. Salam and J. A. Strathdee,Supergauge Transformations, Nucl. Phys. B76 (1974) 477–482

    1974

  35. [43]

    Salam and J

    A. Salam and J. A. Strathdee,On Superfields and Fermi-Bose Symmetry, Phys. Rev. D 11 (1975) 1521–1535

    1975

  36. [44]

    Zumino,Supersymmetry and Kahler Manifolds, Phys

    B. Zumino,Supersymmetry and Kahler Manifolds, Phys. Lett. B87 (1979) 203

    1979

  37. [45]

    Fayet and J

    P. Fayet and J. Iliopoulos,Spontaneously Broken Supergauge Symmetries and 166 Goldstone Spinors, Phys. Lett. B51 (1974) 461–464

    1974

  38. [46]

    O’Raifeartaigh,Spontaneous Symmetry Breaking for Chiral Scalar Superfields, Nucl

    L. O’Raifeartaigh,Spontaneous Symmetry Breaking for Chiral Scalar Superfields, Nucl. Phys. B96 (1975) 331–352

    1975

  39. [47]

    K. A. Intriligator, N. Seiberg and D. Shih,Supersymmetry breaking, R-symmetry breaking and metastable vacua, JHEP 07 (2007) 017, [hep-th/0703281]

    2007 arXiv

  40. [48]

    S. R. Coleman and E. J. Weinberg,Radiative Corrections as the Origin of Spontaneous Symmetry Breaking, Phys. Rev. D7 (1973) 1888–1910

    1973

  41. [49]

    Nambu and G

    Y. Nambu and G. Jona-Lasinio,Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. 1., Phys. Rev.122 (1961) 345–358

    1961

  42. [50]

    Goldstone,Field Theories with Superconductor Solutions, Nuovo Cim.19 (1961) 154–164

    J. Goldstone,Field Theories with Superconductor Solutions, Nuovo Cim.19 (1961) 154–164

    1961

  43. [51]

    Goldstone, A

    J. Goldstone, A. Salam and S. Weinberg,Broken Symmetries, Phys. Rev.127 (1962) 965–970

    1962

  44. [52]

    D. V. Volkov and V. P. Akulov,Is the Neutrino a Goldstone Particle?, Phys. Lett. B 46 (1973) 109–110

    1973

  45. [53]

    Deser and B

    S. Deser and B. Zumino,Broken Supersymmetry and Supergravity, Phys. Rev. Lett.38 (1977) 1433–1436

    1977

  46. [54]

    Fayet,Lower Limit on the Mass of a Light Gravitino from e+ e- Annihilation Experiments, Phys

    P. Fayet,Lower Limit on the Mass of a Light Gravitino from e+ e- Annihilation Experiments, Phys. Lett. B175 (1986) 471–477

    1986

  47. [55]

    Casalbuoni, S

    R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto,A GRAVITINO - GOLDSTINO HIGH-ENERGY EQUIVALENCE THEOREM, Phys. Lett. B215 (1988) 313–316

    1988

  48. [56]

    Casalbuoni, S

    R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto,High-Energy Equivalence Theorem in Spontaneously Broken Supergravity, Phys. Rev. D39 (1989) 2281

    1989

  49. [57]

    Rocek,Linearizing the Volkov-Akulov Model, Phys

    M. Rocek,Linearizing the Volkov-Akulov Model, Phys. Rev. Lett.41 (1978) 451–453

    1978

  50. [58]

    Lindstrom and M

    U. Lindstrom and M. Rocek,CONSTRAINED LOCAL SUPERFIELDS, Phys. Rev. D 19 (1979) 2300–2303

    1979

  51. [59]

    Komargodski and N

    Z. Komargodski and N. Seiberg,From Linear SUSY to Constrained Superfields, JHEP 09 (2009) 066, [0907.2441]

    2009 arXiv

  52. [60]

    Dall’Agata and F

    G. Dall’Agata and F. Farakos,Constrained superfields in Supergravity, JHEP 02 (2016) 101, [1512.02158]

    2016 arXiv

  53. [61]

    Dall’Agata, E

    G. Dall’Agata, E. Dudas and F. Farakos,On the origin of constrained superfields, JHEP 05 (2016) 041, [1603.03416]

    2016 arXiv

  54. [62]

    E. A. Ivanov and A. A. Kapustnikov,General Relationship Between Linear and Nonlinear Realizations of Supersymmetry, J. Phys. A11 (1978) 2375–2384

    1978

  55. [63]

    E. A. Ivanov and A. A. Kapustnikov,THE NONLINEAR REALIZATION STRUCTURE OF MODELS WITH SPONTANEOUSLY BROKEN SUPERSYMMETRY, J. Phys. G8 (1982) 167–191

    1982

  56. [64]

    S. M. Kuzenko and S. J. Tyler,Relating the Komargodski-Seiberg and Akulov-Volkov actions: Exact nonlinear field redefinition, Phys. Lett. B698 (2011) 319–322, [1009.3298]

    2011 arXiv

  57. [65]

    Adams, N

    A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi,Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014, [hep-th/0602178]

    2006 arXiv

  58. [66]

    Bellazzini,Softness and amplitudes’ positivity for spinning particles, JHEP 02 (2017) 034, [1605.06111]

    B. Bellazzini,Softness and amplitudes’ positivity for spinning particles, JHEP 02 (2017) 034, [1605.06111]

    2017 arXiv

  59. [67]

    Ferrara, R

    S. Ferrara, R. Kallosh and J. Thaler,Cosmology with orthogonal nilpotent superfields, Phys. Rev. D93 (2016) 043516, [1512.00545]. 167

    2016 arXiv

  60. [68]

    J. J. M. Carrasco, R. Kallosh and A. Linde,Minimal supergravity inflation, Phys. Rev. D 93 (2016) 061301, [1512.00546]

    2016 arXiv

  61. [69]

    E. W. Kolb, A. J. Long and E. McDonough,Catastrophic production of slow gravitinos, Phys. Rev. D104 (2021) 075015, [2102.10113]

    2021 arXiv

  62. [70]

    Dudas, M

    E. Dudas, M. A. G. Garcia, Y. Mambrini, K. A. Olive, M. Peloso and S. Verner,Slow and Safe Gravitinos, Phys. Rev. D103 (2021) 123519, [2104.03749]

    2021 arXiv

  63. [71]

    Y. Kahn, D. A. Roberts and J. Thaler,The goldstone and goldstino of supersymmetric inflation, JHEP 10 (2015) 001, [1504.05958]

    2015 arXiv

  64. [72]

    M. Dine, G. Festuccia and Z. Komargodski,A Bound on the Superpotential, JHEP 03 (2010) 011, [0910.2527]

    2010 arXiv

  65. [73]

    Bellazzini, L

    B. Bellazzini, L. Martucci and R. Torre,Symmetries, Sum Rules and Constraints on Effective Field Theories, JHEP 09 (2014) 100, [1405.2960]

    2014 arXiv

  66. [74]

    Trott,Causality, unitarity and symmetry in effective field theory, JHEP 07 (2021) 143, [2011.10058]

    T. Trott,Causality, unitarity and symmetry in effective field theory, JHEP 07 (2021) 143, [2011.10058]

    2021 arXiv

  67. [75]

    Benakli, L

    K. Benakli, L. Darmé and Y. Oz,The Slow Gravitino, JHEP 10 (2014) 121, [1407.8321]

    2014 arXiv

  68. [76]

    Hasegawa, K

    F. Hasegawa, K. Mukaida, K. Nakayama, T. Terada and Y. Yamada,Gravitino Problem in Minimal Supergravity Inflation, Phys. Lett. B767 (2017) 392–397, [1701.03106]

    2017 arXiv

  69. [77]

    E. W. Kolb, A. J. Long and E. McDonough,Gravitino Swampland Conjecture, Phys. Rev. Lett.127 (2021) 131603, [2103.10437]

    2021 arXiv

  70. [78]

    Terada,Minimal supergravity inflation without slow gravitino, Phys

    T. Terada,Minimal supergravity inflation without slow gravitino, Phys. Rev. D103 (2021) 125022, [2104.05731]

    2021 arXiv

  71. [79]

    Antoniadis, K

    I. Antoniadis, K. Benakli and W. Ke,Salvage of too slow gravitinos, JHEP 11 (2021) 063, [2105.03784]

    2021 arXiv

  72. [80]

    Alberte, C

    L. Alberte, C. de Rham, S. Jaitly and A. J. Tolley,Positivity Bounds and the Massless Spin-2 Pole, Phys. Rev. D102 (2020) 125023, [2007.12667]

    2020 arXiv

  73. [81]

    Tokuda, K

    J. Tokuda, K. Aoki and S. Hirano,Gravitational positivity bounds, JHEP 11 (2020) 054, [2007.15009]

    2020 arXiv

  74. [82]

    Alberte, C

    L. Alberte, C. de Rham, S. Jaitly and A. J. Tolley,QED positivity bounds, Phys. Rev. D 103 (2021) 125020, [2012.05798]

    2021 arXiv

  75. [83]

    Caron-Huot, D

    S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin,Sharp boundaries for the swampland, JHEP 07 (2021) 110, [2102.08951]

    2021 arXiv

  76. [84]

    Arkani-Hamed, Y.-t

    N. Arkani-Hamed, Y.-t. Huang, J.-Y. Liu and G. N. Remmen,Causality, unitarity, and the weak gravity conjecture, JHEP 03 (2022) 083, [2109.13937]

    2022 arXiv

  77. [85]

    Ferrara and B

    S. Ferrara and B. Zumino,Transformation Properties of the Supercurrent, Nucl. Phys. B 87 (1975) 207

    1975

  78. [86]

    Cremmer, S

    E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen,Coupling Supersymmetric Yang-Mills Theories to Supergravity, Phys. Lett. B116 (1982) 231–237

    1982

  79. [87]

    Cremmer, S

    E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen,Yang-Mills Theories with Local Supersymmetry: Lagrangian, Transformation Laws and SuperHiggs Effect, Nucl. Phys. B212 (1983) 413

    1983

  80. [88]

    J. A. Bagger,Coupling the Gauge Invariant Supersymmetric Nonlinear Sigma Model to Supergravity, Nucl. Phys. B211 (1983) 302

    1983

  81. [89]

    Elvang, D

    H. Elvang, D. Z. Freedman and B. Kors,Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings, JHEP 11 (2006) 068, [hep-th/0606012]

    2006 arXiv

  82. [90]

    De Rydt, J

    J. De Rydt, J. Rosseel, T. T. Schmidt, A. Van Proeyen and M. Zagermann,Symplectic structure of N=1 supergravity with anomalies and Chern-Simons terms, Class. Quant. Grav.24 (2007) 5201–5220, [0705.4216]. 168

    2007 arXiv

  83. [91]

    Binetruy, G

    P. Binetruy, G. Dvali, R. Kallosh and A. Van Proeyen,Fayet-Iliopoulos terms in supergravity and cosmology, Class. Quant. Grav.21 (2004) 3137–3170, [hep-th/0402046]

    2004 arXiv

  84. [92]

    Ferrara and A

    S. Ferrara and A. Van Proeyen,Mass Formulae for Broken Supersymmetry in Curved Space-Time, Fortsch. Phys.64 (2016) 896–902, [1609.08480]

    2016 arXiv

  85. [93]

    E. A. Ivanov and A. A. Kapustnikov,On a Model Independent Description of Spontaneously BrokenN = 1 Supergravity in Superspace, Phys. Lett. B143 (1984) 379–383

    1984

  86. [94]

    E. A. Ivanov and A. A. Kapustnikov,Geometry of Spontaneously Broken LocalN = 1 Supersymmetry in Superspace, Nucl. Phys. B333 (1990) 439–470

    1990

  87. [95]

    Samuel and J

    S. Samuel and J. Wess,A Superfield Formulation of the Nonlinear Realization of Supersymmetry and Its Coupling to Supergravity, Nucl. Phys. B221 (1983) 153–177

    1983

  88. [96]

    Farakos and A

    F. Farakos and A. Kehagias,Decoupling Limits of sGoldstino Modes in Global and Local Supersymmetry, Phys. Lett. B724 (2013) 322–327, [1302.0866]

    2013 arXiv

  89. [97]

    Antoniadis, E

    I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti,The Volkov–Akulov–Starobinsky supergravity, Phys. Lett. B733 (2014) 32–35, [1403.3269]

    2014 arXiv

  90. [98]

    Ferrara, R

    S. Ferrara, R. Kallosh and A. Linde,Cosmology with Nilpotent Superfields, JHEP 10 (2014) 143, [1408.4096]

    2014 arXiv

  91. [99]

    Kallosh and A

    R. Kallosh and A. Linde,Inflation and Uplifting with Nilpotent Superfields, JCAP 01 (2015) 025, [1408.5950]

    2015 arXiv

  92. [100]

    Dall’Agata and F

    G. Dall’Agata and F. Zwirner,On sgoldstino-less supergravity models of inflation, JHEP 12 (2014) 172, [1411.2605]

    2014 arXiv

  93. [101]

    Kallosh, A

    R. Kallosh, A. Linde and M. Scalisi,Inflation, de Sitter Landscape and Super-Higgs effect, JHEP 03 (2015) 111, [1411.5671]

    2015 arXiv

  94. [102]

    Dudas, S

    E. Dudas, S. Ferrara, A. Kehagias and A. Sagnotti,Properties of Nilpotent Supergravity, JHEP 09 (2015) 217, [1507.07842]

    2015 arXiv

  95. [103]

    E. A. Bergshoeff, D. Z. Freedman, R. Kallosh and A. Van Proeyen,Pure de Sitter Supergravity, Phys. Rev. D92 (2015) 085040, [1507.08264]

    2015 arXiv

  96. [104]

    Hasegawa and Y

    F. Hasegawa and Y. Yamada,Component action of nilpotent multiplet coupled to matter in 4 dimensionalN = 1 supergravity, JHEP 10 (2015) 106, [1507.08619]

    2015 arXiv

  97. [105]

    Ferrara, M

    S. Ferrara, M. Porrati and A. Sagnotti,Scale invariant Volkov–Akulov supergravity, Phys. Lett. B749 (2015) 589–591, [1508.02939]

    2015 arXiv

  98. [106]

    S. M. Kuzenko,Complex linear Goldstino superfield and supergravity, JHEP 10 (2015) 006, [1508.03190]

    2015 arXiv

  99. [107]

    Antoniadis and C

    I. Antoniadis and C. Markou,The coupling of Non-linear Supersymmetry to Supergravity, Eur. Phys. J. C75 (2015) 582, [1508.06767]

    2015 arXiv

  100. [108]

    Kallosh and T

    R. Kallosh and T. Wrase,De Sitter Supergravity Model Building, Phys. Rev. D92 (2015) 105010, [1509.02137]

    2015 arXiv

  101. [109]

    Kallosh,Matter-coupled de Sitter Supergravity, Theor

    R. Kallosh,Matter-coupled de Sitter Supergravity, Theor. Math. Phys.187 (2016) 695–705, [1509.02136]

    2016 arXiv

  102. [110]

    Dall’Agata, S

    G. Dall’Agata, S. Ferrara and F. Zwirner,Minimal scalar-less matter-coupled supergravity, Phys. Lett. B752 (2016) 263–266, [1509.06345]

    2016 arXiv

  103. [111]

    Bandos, L

    I. Bandos, L. Martucci, D. Sorokin and M. Tonin,Brane induced supersymmetry breaking and de Sitter supergravity, JHEP 02 (2016) 080, [1511.03024]

    2016 arXiv

  104. [112]

    Bandos, M

    I. Bandos, M. Heller, S. M. Kuzenko, L. Martucci and D. Sorokin,The Goldstino brane, the constrained superfields and matter inN = 1 supergravity, JHEP 11 (2016) 109, [1608.05908]

    2016 arXiv

  105. [113]

    Kallosh, L

    R. Kallosh, L. Kofman, A. D. Linde and A. Van Proeyen,Gravitino production after inflation, Phys. Rev. D61 (2000) 103503, [hep-th/9907124]. 169

    2000 arXiv

  106. [114]

    Kallosh, L

    R. Kallosh, L. Kofman, A. D. Linde and A. Van Proeyen,Superconformal symmetry, supergravity and cosmology, Class. Quant. Grav.17 (2000) 4269–4338, [hep-th/0006179]

    2000 arXiv

  107. [115]

    G. F. Giudice, I. Tkachev and A. Riotto,Nonthermal production of dangerous relics in the early universe, JHEP 08 (1999) 009, [hep-ph/9907510]

    1999 arXiv

  108. [116]

    G. F. Giudice, A. Riotto and I. Tkachev,Thermal and nonthermal production of gravitinos in the early universe, JHEP 11 (1999) 036, [hep-ph/9911302]

    1999 arXiv

  109. [117]

    H. P. Nilles, M. Peloso and L. Sorbo,Coupled fields in external background with application to nonthermal production of gravitinos, JHEP 04 (2001) 004, [hep-th/0103202]

    2001 arXiv

  110. [118]

    H. P. Nilles, M. Peloso and L. Sorbo,Nonthermal production of gravitinos and inflatinos, Phys. Rev. Lett.87 (2001) 051302, [hep-ph/0102264]

    2001 arXiv

  111. [119]

    Parker,Quantized fields and particle creation in expanding universes

    L. Parker,Quantized fields and particle creation in expanding universes. 1., Phys. Rev. 183 (1969) 1057–1068

    1969

  112. [120]

    Y. B. Zeldovich and A. A. Starobinsky,Particle production and vacuum polarization in an anisotropic gravitational field, Zh. Eksp. Teor. Fiz.61 (1971) 2161–2175

    1971

  113. [121]

    L. H. Ford,Gravitational Particle Creation and Inflation, Phys. Rev. D35 (1987) 2955

    1987

  114. [122]

    N. D. Birrell and P. C. W. Davies,Quantum Fields in Curved Space. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge, UK, 1982, 10.1017/CBO9780511622632

    1982 doi

  115. [123]

    D. S. Gorbunov and V. A. Rubakov,Introduction to the theory of the early universe: Cosmological perturbations and inflationary theory. 2011, 10.1142/7873

    2011 doi

  116. [124]

    Kofman, A

    L. Kofman, A. D. Linde and A. A. Starobinsky,Reheating after inflation, Phys. Rev. Lett.73 (1994) 3195–3198, [hep-th/9405187]

    1994 arXiv

  117. [125]

    Kofman, A

    L. Kofman, A. D. Linde and A. A. Starobinsky,Towards the theory of reheating after inflation, Phys. Rev. D56 (1997) 3258–3295, [hep-ph/9704452]

    1997 arXiv

  118. [126]

    Vafa,The String landscape and the swampland, hep-th/0509212

    C. Vafa,The String landscape and the swampland, hep-th/0509212

    arXiv

  119. [127]

    Palti,The Swampland: Introduction and Review, Fortsch

    E. Palti,The Swampland: Introduction and Review, Fortsch. Phys.67 (2019) 1900037, [1903.06239]

    2019 arXiv

  120. [128]

    S. A. Fulling,REMARKS ON POSITIVE FREQUENCY AND HAMILTONIANS IN EXPANDING UNIVERSES, Gen. Rel. Grav.10 (1979) 807–824

    1979

  121. [129]

    Weiss,Consistency of Hamiltonian Diagonalization for Field Theories in a Robertson-walker Background, Phys

    N. Weiss,Consistency of Hamiltonian Diagonalization for Field Theories in a Robertson-walker Background, Phys. Rev. D34 (1986) 1768

    1986

  122. [130]

    Bozza, M

    V. Bozza, M. Giovannini and G. Veneziano,Cosmological perturbations from a new physics hypersurface, JCAP 05 (2003) 001, [hep-th/0302184]

    2003 arXiv

  123. [131]

    Grain and V

    J. Grain and V. Vennin,Canonical transformations and squeezing formalism in cosmology, JCAP 02 (2020) 022, [1910.01916]

    2020 arXiv

  124. [132]

    Peloso and L

    M. Peloso and L. Sorbo,Preheating of massive fermions after inflation: Analytical results, JHEP 05 (2000) 016, [hep-ph/0003045]

    2000 arXiv

  125. [133]

    D. J. H. Chung, L. L. Everett, H. Yoo and P. Zhou,Gravitational Fermion Production in Inflationary Cosmology, Phys. Lett. B712 (2012) 147–154, [1109.2524]

    2012 arXiv

  126. [134]

    Himmetoglu, C

    B. Himmetoglu, C. R. Contaldi and M. Peloso,Instability of anisotropic cosmological solutions supported by vector fields, Phys. Rev. Lett.102 (2009) 111301, [0809.2779]

    2009 arXiv

  127. [135]

    P. W. Graham, J. Mardon and S. Rajendran,Vector Dark Matter from Inflationary Fluctuations, Phys. Rev. D93 (2016) 103520, [1504.02102]

    2016 arXiv

  128. [136]

    Ahmed, B

    A. Ahmed, B. Grzadkowski and A. Socha,Gravitational production of vector dark matter, JHEP 08 (2020) 059, [2005.01766]

    2020 arXiv

  129. [137]

    Wess and B

    J. Wess and B. Zumino,Superspace Formulation of Supergravity, Phys. Lett. B66 170 (1977) 361–364

    1977

  130. [138]

    Grimm, J

    R. Grimm, J. Wess and B. Zumino,Consistency Checks on the Superspace Formulation of Supergravity, Phys. Lett. B73 (1978) 415–417

    1978

  131. [139]

    Wess and B

    J. Wess and B. Zumino,Superfield Lagrangian for Supergravity, Phys. Lett. B74 (1978) 51–53

    1978

  132. [140]

    Siegel and S

    W. Siegel and S. J. Gates, Jr.,Superfield Supergravity, Nucl. Phys. B147 (1979) 77–104

    1979

  133. [141]

    K. S. Stelle and P. C. West,Minimal Auxiliary Fields for Supergravity, Phys. Lett. B 74 (1978) 330–332

    1978

  134. [142]

    Ferrara and P

    S. Ferrara and P. van Nieuwenhuizen,The Auxiliary Fields of Supergravity, Phys. Lett. B 74 (1978) 333

    1978

  135. [143]

    M. F. Sohnius and P. C. West,An Alternative Minimal Off-Shell Version of N=1 Supergravity, Phys. Lett. B105 (1981) 353–357

    1981

  136. [144]

    Ferrara and B

    S. Ferrara and B. Zumino,Structure of Conformal Supergravity, Nucl. Phys. B134 (1978) 301–326

    1978

  137. [145]

    Komargodski and N

    Z. Komargodski and N. Seiberg,Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity, JHEP 07 (2010) 017, [1002.2228]

    2010 arXiv

  138. [146]

    Festuccia and N

    G. Festuccia and N. Seiberg,Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114, [1105.0689]

    2011 arXiv

  139. [147]

    T. E. Clark and S. T. Love,The Supercurrent in supersymmetric field theories, Int. J. Mod. Phys. A11 (1996) 2807–2823, [hep-th/9506145]

    1996 arXiv

  140. [148]

    Komargodski and N

    Z. Komargodski and N. Seiberg,Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity, JHEP 06 (2009) 007, [0904.1159]

    2009 arXiv

  141. [149]

    Fierz and W

    M. Fierz and W. Pauli,On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A173 (1939) 211–232

    1939

  142. [150]

    D. G. Boulware and S. Deser,Can gravitation have a finite range?, Phys. Rev. D6 (1972) 3368–3382

    1972

  143. [151]

    Bouatta, G

    N. Bouatta, G. Compere and A. Sagnotti,An Introduction to free higher-spin fields, in 1st Solvay Workshop on Higher Spin Gauge Theories, pp. 79–99, 9, 2004. hep-th/0409068

    2004 arXiv

  144. [152]

    Hinterbichler,Theoretical Aspects of Massive Gravity, Rev

    K. Hinterbichler,Theoretical Aspects of Massive Gravity, Rev. Mod. Phys.84 (2012) 671–710, [1105.3735]

    2012 arXiv

  145. [153]

    Arkani-Hamed, H

    N. Arkani-Hamed, H. Georgi and M. D. Schwartz,Effective field theory for massive gravitons and gravity in theory space, Annals Phys.305 (2003) 96–118, [hep-th/0210184]

    2003 arXiv

  146. [154]

    Arkani-Hamed and M

    N. Arkani-Hamed and M. D. Schwartz,Discrete gravitational dimensions, Phys. Rev. D 69 (2004) 104001, [hep-th/0302110]

    2004 arXiv

  147. [155]

    M. D. Schwartz,Constructing gravitational dimensions, Phys. Rev. D68 (2003) 024029, [hep-th/0303114]

    2003 arXiv

  148. [156]

    Bonifacio and K

    J. Bonifacio and K. Hinterbichler,Bounds on Amplitudes in Effective Theories with Massive Spinning Particles, Phys. Rev. D98 (2018) 045003, [1804.08686]

    2018 arXiv

  149. [157]

    Bonifacio and K

    J. Bonifacio and K. Hinterbichler,Universal bound on the strong coupling scale of a gravitationally coupled massive spin-2 particle, Phys. Rev. D98 (2018) 085006, [1806.10607]

    2018 arXiv

  150. [158]

    Bonifacio, K

    J. Bonifacio, K. Hinterbichler and R. A. Rosen,Constraints on a gravitational Higgs mechanism, Phys. Rev. D100 (2019) 084017, [1903.09643]

    2019 arXiv

  151. [159]

    Kundu, E

    S. Kundu, E. Palti and J. Quirant,Regge growth of isolated massive spin-2 particles and the Swampland, JHEP 05 (2024) 139, [2311.00022]

    2024 arXiv

  152. [160]

    de Rham and G

    C. de Rham and G. Gabadadze,Generalization of the Fierz-Pauli Action, Phys. Rev. 171 D 82 (2010) 044020, [1007.0443]

    2010 arXiv

  153. [161]

    de Rham, G

    C. de Rham, G. Gabadadze and A. J. Tolley,Resummation of Massive Gravity, Phys. Rev. Lett.106 (2011) 231101, [1011.1232]

    2011 arXiv

  154. [162]

    S. F. Hassan and R. A. Rosen,Bimetric Gravity from Ghost-free Massive Gravity, JHEP 02 (2012) 126, [1109.3515]

    2012 arXiv

  155. [163]

    Sekhar Chivukula, D

    R. Sekhar Chivukula, D. Foren, K. A. Mohan, D. Sengupta and E. H. Simmons, Scattering amplitudes of massive spin-2 Kaluza-Klein states grow only asO(s), Phys. Rev. D101 (2020) 055013, [1906.11098]

    2020 arXiv

  156. [164]

    R. S. Chivukula, D. Foren, K. A. Mohan, D. Sengupta and E. H. Simmons,Massive Spin-2 Scattering Amplitudes in Extra-Dimensional Theories, Phys. Rev. D101 (2020) 075013, [2002.12458]

    2020 arXiv

  157. [165]

    Bonifacio and K

    J. Bonifacio and K. Hinterbichler,Unitarization from Geometry, JHEP 12 (2019) 165, [1910.04767]

    2019 arXiv

  158. [166]

    I. L. Buchbinder, S. J. Gates, Jr., W. D. Linch, III and J. Phillips,New 4-D, N=1 superfield theory: Model of free massive superspin 3/2 multiplet, Phys. Lett. B535 (2002) 280–288, [hep-th/0201096]

    2002 arXiv

  159. [167]

    Y. M. Zinoviev,Massive spin two supermultiplets, hep-th/0206209

    arXiv

  160. [168]

    Del Monte, D

    F. Del Monte, D. Francia and P. A. Grassi,Multimetric Supergravities, JHEP 09 (2016) 064, [1605.06793]

    2016 arXiv

  161. [169]

    Y. M. Zinoviev,On massive super(bi)gravity in the constructive approach, Class. Quant. Grav.35 (2018) 175006, [1805.01650]

    2018 arXiv

  162. [170]

    Engelbrecht, C

    L. Engelbrecht, C. R. T. Jones and S. Paranjape,Supersymmetric Massive Gravity, JHEP 10 (2022) 130, [2205.12982]

    2022 arXiv

  163. [171]

    Gunaydin, G

    M. Gunaydin, G. Sierra and P. K. Townsend,The Geometry of N=2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B242 (1984) 244–268

    1984

  164. [172]

    Ceresole and G

    A. Ceresole and G. Dall’Agata,General matter coupled N=2, D = 5 gauged supergravity, Nucl. Phys. B585 (2000) 143–170, [hep-th/0004111]

    2000 arXiv

  165. [173]

    A. N. Petrov, S. M. Kopeikin, R. R. Lompay and B. Tekin,Metric Theories of Gravity: Perturbations and Conservation Laws, vol. 38 ofDe Gruyter Studies in Mathematical Physics. De Gruyter, 4, 2017, 10.1515/9783110351781

    2017 doi

  166. [174]

    C. G. Callan, Jr., S. R. Coleman and R. Jackiw,A New improved energy - momentum tensor, Annals Phys.59 (1970) 42–73

    1970

  167. [175]

    Zucker,Minimal off-shell supergravity in five-dimensions, Nucl

    M. Zucker,Minimal off-shell supergravity in five-dimensions, Nucl. Phys. B570 (2000) 267–283, [hep-th/9907082]

    2000 arXiv

  168. [176]

    Gherghetta and A

    T. Gherghetta and A. Pomarol,A Stuckelberg formalism for the gravitino from warped extra dimensions, Phys. Lett. B536 (2002) 277–282, [hep-th/0203120]

    2002 arXiv

  169. [177]

    X. O. Camanho, J. D. Edelstein, J. Maldacena and A. Zhiboedov,Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020, [1407.5597]

    2016 arXiv

  170. [178]

    D. Lust, C. Markou, P. Mazloumi and S. Stieberger,Extracting bigravity from string theory, JHEP 12 (2021) 220, [2106.04614]

    2021 arXiv

  171. [179]

    I. L. Buchbinder, D. M. Gitman, V. A. Krykhtin and V. D. Pershin,Equations of motion for massive spin-2 field coupled to gravity, Nucl. Phys. B584 (2000) 615–640, [hep-th/9910188]

    2000 arXiv

  172. [180]

    Ooguri and C

    H. Ooguri and C. Vafa,On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B766 (2007) 21–33, [hep-th/0605264]

    2007 arXiv

  173. [181]

    Adams, O

    A. Adams, O. DeWolfe and W. Taylor,String universality in ten dimensions, Phys. Rev. Lett.105 (2010) 071601, [1006.1352]

    2010 arXiv

  174. [182]

    Kim, H.-C

    H.-C. Kim, H.-C. Tarazi and C. Vafa,Four-dimensional N = 4 SYM theory and the 172 swampland, Phys. Rev. D102 (2020) 026003, [1912.06144]

    2020 arXiv

  175. [183]

    H.-C. Kim, G. Shiu and C. Vafa,Branes and the Swampland, Phys. Rev. D100 (2019) 066006, [1905.08261]

    2019 arXiv

  176. [184]

    Bedroya, Y

    A. Bedroya, Y. Hamada, M. Montero and C. Vafa,Compactness of brane moduli and the String Lamppost Principle in d> 6, JHEP 02 (2022) 082, [2110.10157]

    2022 arXiv

  177. [185]

    Montero and C

    M. Montero and C. Vafa,Cobordism Conjecture, Anomalies, and the String Lamppost Principle, JHEP 01 (2021) 063, [2008.11729]

    2021 arXiv

  178. [186]

    Polchinski,String theory

    J. Polchinski,String theory. Vol. 1: An introduction to the bosonic string. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 12, 2007, 10.1017/CBO9780511816079

    2007 doi

  179. [187]

    Polchinski,String theory

    J. Polchinski,String theory. Vol. 2: Superstring theory and beyond. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 12, 2007, 10.1017/CBO9780511618123

    2007 doi

  180. [188]

    M. B. Green, J. H. Schwarz and E. Witten,SUPERSTRING THEORY. VOL. 2: LOOP AMPLITUDES, ANOMALIES AND PHENOMENOLOGY. 7, 1988

    1988

  181. [189]

    M. B. Green, J. H. Schwarz and E. Witten,SUPERSTRING THEORY. VOL. 1: INTRODUCTION. Cambridge Monographs on Mathematical Physics. 7, 1988

    1988

  182. [190]

    Becker, M

    K. Becker, M. Becker and J. H. Schwarz,String theory and M-theory: A modern introduction. Cambridge University Press, 12, 2006, 10.1017/CBO9780511816086

    2006 doi

  183. [191]

    Angelantonj and A

    C. Angelantonj and A. Sagnotti,Open strings, Phys. Rept.371 (2002) 1–150, [hep-th/0204089]

    2002 arXiv

  184. [192]

    Dudas,Theory and phenomenology of type I strings and M theory, Class

    E. Dudas,Theory and phenomenology of type I strings and M theory, Class. Quant. Grav.17 (2000) R41–R116, [hep-ph/0006190]

    2000 arXiv

  185. [193]

    Angelantonj and I

    C. Angelantonj and I. Florakis,A Lightning Introduction to String Theory, 2406.09508

  186. [194]

    Goddard, J

    P. Goddard, J. Goldstone, C. Rebbi and C. B. Thorn,Quantum dynamics of a massless relativistic string, Nucl. Phys. B56 (1973) 109–135

    1973

  187. [195]

    C. G. Callan, Jr., E. J. Martinec, M. J. Perry and D. Friedan,Strings in Background Fields, Nucl. Phys. B262 (1985) 593–609

    1985

  188. [196]

    A. M. Polyakov,Quantum Geometry of Bosonic Strings, Phys. Lett. B103 (1981) 207–210

    1981

  189. [197]

    A. M. Polyakov,Quantum Geometry of Fermionic Strings, Phys. Lett. B103 (1981) 211–213

    1981

  190. [198]

    Brink, P

    L. Brink, P. Di Vecchia and P. S. Howe,A Locally Supersymmetric and Reparametrization Invariant Action for the Spinning String, Phys. Lett. B65 (1976) 471–474

    1976

  191. [199]

    Deser and B

    S. Deser and B. Zumino,A Complete Action for the Spinning String, Phys. Lett. B65 (1976) 369–373

    1976

  192. [200]

    Ramond,Dual Theory for Free Fermions, Phys

    P. Ramond,Dual Theory for Free Fermions, Phys. Rev. D3 (1971) 2415–2418

    1971

  193. [201]

    Neveu and J

    A. Neveu and J. H. Schwarz,Tachyon-free dual model with a positive-intercept trajectory, Phys. Lett. B34 (1971) 517–518

    1971

  194. [202]

    Ramond,An Interpretation of Dual Theories, Nuovo Cim

    P. Ramond,An Interpretation of Dual Theories, Nuovo Cim. A4 (1971) 544–548

    1971

  195. [203]

    Neveu and J

    A. Neveu and J. H. Schwarz,Factorizable dual model of pions, Nucl. Phys. B31 (1971) 86–112

    1971

  196. [204]

    Neveu and J

    A. Neveu and J. H. Schwarz,Quark Model of Dual Pions, Phys. Rev. D4 (1971) 1109–1111

    1971

  197. [205]

    Neveu, J

    A. Neveu, J. H. Schwarz and C. B. Thorn,Reformulation of the Dual Pion Model, Phys. Lett. B35 (1971) 529–533

    1971

  198. [206]

    Gliozzi, J

    F. Gliozzi, J. Scherk and D. I. Olive,Supersymmetry, Supergravity Theories and the 173 Dual Spinor Model, Nucl. Phys. B122 (1977) 253–290

    1977

  199. [207]

    Alvarez-Gaume and E

    L. Alvarez-Gaume and E. Witten,Gravitational Anomalies, Nucl. Phys. B234 (1984) 269

    1984

  200. [208]

    A. N. Schellekens and N. P. Warner,Anomalies and Modular Invariance in String Theory, Phys. Lett. B177 (1986) 317–323

    1986

  201. [209]

    A. N. Schellekens and N. P. Warner,Anomalies, Characters and Strings, Nucl. Phys. B 287 (1987) 317

    1987

  202. [210]

    Lerche, B

    W. Lerche, B. E. W. Nilsson and A. N. Schellekens,Heterotic String Loop Calculation of the Anomaly Cancelling Term, Nucl. Phys. B289 (1987) 609

    1987

  203. [211]

    Bianchi and A

    M. Bianchi and A. Sagnotti,On the systematics of open string theories, Phys. Lett. B 247 (1990) 517–524

    1990

  204. [212]

    L. J. Dixon and J. A. Harvey,String Theories in Ten-Dimensions Without Space-Time Supersymmetry, Nucl. Phys. B274 (1986) 93–105

    1986

  205. [213]

    Seiberg and E

    N. Seiberg and E. Witten,Spin Structures in String Theory, Nucl. Phys. B276 (1986) 272

    1986

  206. [214]

    J. Dai, R. G. Leigh and J. Polchinski,New Connections Between String Theories, Mod. Phys. Lett. A4 (1989) 2073–2083

    1989

  207. [215]

    R. G. Leigh,Dirac-Born-Infeld Action from Dirichlet Sigma Model, Mod. Phys. Lett. A 4 (1989) 2767

    1989

  208. [216]

    Horava,Background Duality of Open String Models, Phys

    P. Horava,Background Duality of Open String Models, Phys. Lett. B231 (1989) 251–257

    1989

  209. [217]

    Polchinski,Dirichlet Branes and Ramond-Ramond charges, Phys

    J. Polchinski,Dirichlet Branes and Ramond-Ramond charges, Phys. Rev. Lett.75 (1995) 4724–4727, [hep-th/9510017]

    1995 arXiv

  210. [218]

    C. M. Hull and P. K. Townsend,Unity of superstring dualities, Nucl. Phys. B438 (1995) 109–137, [hep-th/9410167]

    1995 arXiv

  211. [219]

    P. K. Townsend and P. V. Landshoff,The eleven-dimensional supermembrane revisited, Phys. Lett. B350 (1995) 184–187, [hep-th/9501068]

    1995 arXiv

  212. [220]

    M. J. Duff, R. R. Khuri and J. X. Lu,String solitons, Phys. Rept.259 (1995) 213–326, [hep-th/9412184]

    1995 arXiv

  213. [221]

    Polchinski,Tasi lectures on D-branes, inTheoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, pp

    J. Polchinski,Tasi lectures on D-branes, inTheoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, pp. 293–356, 11,

  214. [222]

    C. P. Bachas,Lectures on D-branes, inA Newton Institute Euroconference on Duality and Supersymmetric Theories, pp. 414–473, 6, 1998.hep-th/9806199

    1998 arXiv

  215. [223]

    Polchinski and Y

    J. Polchinski and Y. Cai,Consistency of Open Superstring Theories, Nucl. Phys. B 296 (1988) 91–128

    1988

  216. [224]

    Sagnotti,Open Strings and their Symmetry Groups, inNATO Advanced Summer Institute on Nonperturbative Quantum Field Theory (Cargese Summer Institute), 9,

    A. Sagnotti,Open Strings and their Symmetry Groups, inNATO Advanced Summer Institute on Nonperturbative Quantum Field Theory (Cargese Summer Institute), 9,

  217. [225]

    Bianchi and A

    M. Bianchi and A. Sagnotti,The Partition Function of the SO(8192) Bosonic String, Phys. Lett. B211 (1988) 407–416

    1988

  218. [226]

    Horava,Strings on World Sheet Orbifolds, Nucl

    P. Horava,Strings on World Sheet Orbifolds, Nucl. Phys. B327 (1989) 461–484

    1989

  219. [227]

    Bianchi, G

    M. Bianchi, G. Pradisi and A. Sagnotti,Toroidal compactification and symmetry breaking in open string theories, Nucl. Phys. B376 (1992) 365–386

    1992

  220. [228]

    Witten,Bound states of strings and p-branes, Nucl

    E. Witten,Bound states of strings and p-branes, Nucl. Phys. B460 (1996) 335–350, [hep-th/9510135]

    1996 arXiv

  221. [229]

    J. E. Paton and H.-M. Chan,Generalized veneziano model with isospin, Nucl. Phys. B 10 (1969) 516–520

    1969

  222. [230]

    Marcus and A

    N. Marcus and A. Sagnotti,Group Theory from Quarks at the Ends of Strings, Phys. 174 Lett. B188 (1987) 58–64

    1987

  223. [231]

    Pradisi and A

    G. Pradisi and A. Sagnotti,Open String Orbifolds, Phys. Lett. B216 (1989) 59–67

    1989

  224. [232]

    Bianchi and A

    M. Bianchi and A. Sagnotti,Twist symmetry and open string Wilson lines, Nucl. Phys. B361 (1991) 519–538

    1991

  225. [233]

    M. B. Green and J. H. Schwarz,Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory, Phys. Lett. B149 (1984) 117–122

    1984

  226. [234]

    J. A. Harvey and J. A. Minahan,OPEN STRINGS ON ORBIFOLDS, Phys. Lett. B 188 (1987) 44

    1987

  227. [235]

    Ishibashi and T

    N. Ishibashi and T. Onogi,OPEN STRING MODEL BUILDING, Nucl. Phys. B318 (1989) 239–280

    1989

  228. [236]

    Angelantonj, M

    C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y. S. Stanev,Chiral asymmetry in four-dimensional open string vacua, Phys. Lett. B385 (1996) 96–102, [hep-th/9606169]

    1996 arXiv

  229. [237]

    Kakushadze and G

    Z. Kakushadze and G. Shiu,A Chiral N=1 type I vacuum in four-dimensions and its heterotic dual, Phys. Rev. D56 (1997) 3686–3697, [hep-th/9705163]

    1997 arXiv

  230. [238]

    Kakushadze and G

    Z. Kakushadze and G. Shiu,4-D chiral N=1 type one vacua with and without D5-branes, Nucl. Phys. B520 (1998) 75–92, [hep-th/9706051]

    1998 arXiv

  231. [239]

    Kakushadze,On four-dimensional N=1 type I compactifications, Nucl

    Z. Kakushadze,On four-dimensional N=1 type I compactifications, Nucl. Phys. B535 (1998) 311–334, [hep-th/9806008]

    1998 arXiv

  232. [240]

    Kakushadze, G

    Z. Kakushadze, G. Shiu and S. H. H. Tye,Type IIB orientifolds, F theory, type I strings on orbifolds and type I - Heterotic duality, Nucl. Phys. B533 (1998) 25–87, [hep-th/9804092]

    1998 arXiv

  233. [241]

    Zwart,Four-dimensional N=1 Z(N) x Z(M) orientifolds, Nucl

    G. Zwart,Four-dimensional N=1 Z(N) x Z(M) orientifolds, Nucl. Phys. B526 (1998) 378–392, [hep-th/9708040]

    1998 arXiv

  234. [242]

    Klein and R

    M. Klein and R. Rabadan,Z(N) x Z(M) orientifolds with and without discrete torsion, JHEP 10 (2000) 049, [hep-th/0008173]

    2000 arXiv

  235. [243]

    Blumenhagen, L

    R. Blumenhagen, L. Gorlich and B. Kors,Supersymmetric orientifolds in 6-D with D-branes at angles, Nucl. Phys. B569 (2000) 209–228, [hep-th/9908130]

    2000 arXiv

  236. [244]

    Cvetic, M

    M. Cvetic, M. Plumacher and J. Wang,Three family type IIB orientifold string vacua with nonAbelian Wilson lines, JHEP 04 (2000) 004, [hep-th/9911021]

    2000 arXiv

  237. [245]

    Blumenhagen, L

    R. Blumenhagen, L. Gorlich and B. Kors,Supersymmetric 4-D orientifolds of type IIA with D6-branes at angles, JHEP 01 (2000) 040, [hep-th/9912204]

    2000 arXiv

  238. [246]

    Pradisi,Type I vacua from diagonal Z(3) orbifolds, Nucl

    G. Pradisi,Type I vacua from diagonal Z(3) orbifolds, Nucl. Phys. B575 (2000) 134–150, [hep-th/9912218]

    2000 arXiv

  239. [247]

    Cvetic and P

    M. Cvetic and P. Langacker,D = 4 N=1 type IIB orientifolds with continuous Wilson lines, moving branes, and their field theory realization, Nucl. Phys. B586 (2000) 287–302, [hep-th/0006049]

    2000 arXiv

  240. [248]

    Cvetic, A

    M. Cvetic, A. M. Uranga and J. Wang,Discrete Wilson lines in N=1 D = 4 type IIB orientifolds: A Systematic exploration for Z(6) orientifold, Nucl. Phys. B595 (2001) 63–92, [hep-th/0010091]

    2001 arXiv

  241. [249]

    Sagnotti,A Note on the Green-Schwarz mechanism in open string theories, Phys

    A. Sagnotti,A Note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B294 (1992) 196–203, [hep-th/9210127]

    1992 arXiv

  242. [250]

    Scherk and J

    J. Scherk and J. H. Schwarz,Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett. B82 (1979) 60–64

    1979

  243. [251]

    Scherk and J

    J. Scherk and J. H. Schwarz,How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61–88

    1979

  244. [252]

    Cremmer, J

    E. Cremmer, J. Scherk and J. H. Schwarz,Spontaneously Broken N=8 Supergravity, Phys. Lett. B84 (1979) 83–86

    1979

  245. [253]

    J. D. Blum and K. R. Dienes,Strong / weak coupling duality relations for 175 nonsupersymmetric string theories, Nucl. Phys. B516 (1998) 83–159, [hep-th/9707160]

    1998 arXiv

  246. [254]

    J. D. Blum and K. R. Dienes,Duality without supersymmetry: The Case of the SO(16)× SO(16) string, Phys. Lett. B414 (1997) 260–268, [hep-th/9707148]

    1997 arXiv

  247. [255]

    Antoniadis, E

    I. Antoniadis, E. Dudas and A. Sagnotti,Supersymmetry breaking, open strings and M theory, Nucl. Phys. B544 (1999) 469–502, [hep-th/9807011]

    1999 arXiv

  248. [256]

    Antoniadis, G

    I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti,Partial breaking of supersymmetry, open strings and M theory, Nucl. Phys. B553 (1999) 133–154, [hep-th/9812118]

    1999 arXiv

  249. [257]

    A. L. Cotrone,A Z2 × Z2 orientifold with spontaneously broken supersymmetry, Mod. Phys. Lett. A14 (1999) 2487–2497, [hep-th/9909116]

    1999 arXiv

  250. [258]

    Angelantonj and I

    C. Angelantonj and I. Antoniadis,Suppressing the cosmological constant in nonsupersymmetric type I strings, Nucl. Phys. B676 (2004) 129–148, [hep-th/0307254]

    2004 arXiv

  251. [259]

    Angelantonj, M

    C. Angelantonj, M. Cardella and N. Irges,An Alternative for Moduli Stabilisation, Phys. Lett. B641 (2006) 474–480, [hep-th/0608022]

    2006 arXiv

  252. [260]

    S. Abel, E. Dudas, D. Lewis and H. Partouche,Stability and vacuum energy in open string models with broken supersymmetry, JHEP 10 (2019) 226, [1812.09714]

    2019 arXiv

  253. [261]

    Antoniadis, G

    I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti,Open descendants of Z2 × Z2 freely acting orbifolds, Nucl. Phys. B565 (2000) 123–156, [hep-th/9907184]

    2000 arXiv

  254. [262]

    Rohm,Spontaneous Supersymmetry Breaking in Supersymmetric String Theories, Nucl

    R. Rohm,Spontaneous Supersymmetry Breaking in Supersymmetric String Theories, Nucl. Phys. B237 (1984) 553–572

    1984

  255. [263]

    Kounnas and M

    C. Kounnas and M. Porrati,Spontaneous Supersymmetry Breaking in String Theory, Nucl. Phys. B310 (1988) 355–370

    1988

  256. [264]

    Ferrara, C

    S. Ferrara, C. Kounnas, M. Porrati and F. Zwirner,Superstrings with Spontaneously Broken Supersymmetry and their Effective Theories, Nucl. Phys. B318 (1989) 75–105

    1989

  257. [265]

    Kounnas and B

    C. Kounnas and B. Rostand,Coordinate Dependent Compactifications and Discrete Symmetries, Nucl. Phys. B341 (1990) 641–665

    1990

  258. [266]

    Antoniadis and C

    I. Antoniadis and C. Kounnas,Superstring phase transition at high temperature, Phys. Lett. B261 (1991) 369–378

    1991

  259. [267]

    Kiritsis and C

    E. Kiritsis and C. Kounnas,Perturbative and nonperturbative partial supersymmetry breaking: N = 4 → N = 2 → N = 1, Nucl. Phys. B503 (1997) 117–156, [hep-th/9703059]

    1997 arXiv

  260. [268]

    E. S. Fradkin and A. A. Tseytlin,Nonlinear Electrodynamics from Quantized Strings, Phys. Lett. B163 (1985) 123–130

    1985

  261. [269]

    Abouelsaood, C

    A. Abouelsaood, C. G. Callan, Jr., C. R. Nappi and S. A. Yost,Open strings in background gauge fields, Nucl. Phys. B280 (1987) 599–624

    1987

  262. [270]

    Bachas,A Way to break supersymmetry, hep-th/9503030

    C. Bachas,A Way to break supersymmetry, hep-th/9503030

    arXiv

  263. [271]

    Bianchi and Y

    M. Bianchi and Y. S. Stanev,Open strings on the Neveu-Schwarz penta-brane, Nucl. Phys. B523 (1998) 193–210, [hep-th/9711069]

    1998 arXiv

  264. [272]

    Sugimoto,Anomaly cancellations in type I D9 – anti-D9 system and the USp(32) string theory, Prog

    S. Sugimoto,Anomaly cancellations in type I D9 – anti-D9 system and the USp(32) string theory, Prog. Theor. Phys.102 (1999) 685–699, [hep-th/9905159]

    1999 arXiv

  265. [273]

    Antoniadis, E

    I. Antoniadis, E. Dudas and A. Sagnotti,Brane supersymmetry breaking, Phys. Lett. B 464 (1999) 38–45, [hep-th/9908023]

    1999 arXiv

  266. [274]

    Angelantonj,Comments on open string orbifolds with a nonvanishing B(ab), Nucl

    C. Angelantonj,Comments on open string orbifolds with a nonvanishing B(ab), Nucl. Phys. B566 (2000) 126–150, [hep-th/9908064]

    2000 arXiv

  267. [275]

    Aldazabal and A

    G. Aldazabal and A. M. Uranga,Tachyon free nonsupersymmetric type IIB orientifolds via Brane - anti-brane systems, JHEP 10 (1999) 024, [hep-th/9908072]

    1999 arXiv

  268. [276]

    Angelantonj, I

    C. Angelantonj, I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti,Type I 176 vacua with brane supersymmetry breaking, Nucl. Phys. B572 (2000) 36–70, [hep-th/9911081]

    2000 arXiv

  269. [277]

    Angelantonj, C

    C. Angelantonj, C. Condeescu, E. Dudas and G. Leone,Rigid vacua with Brane Supersymmetry Breaking, JHEP 04 (2024) 103, [2403.02392]

    2024 arXiv

  270. [278]

    Dudas and J

    E. Dudas and J. Mourad,Consistent gravitino couplings in nonsupersymmetric strings, Phys. Lett. B514 (2001) 173–182, [hep-th/0012071]

    2001 arXiv

  271. [279]

    Pradisi and F

    G. Pradisi and F. Riccioni,Geometric couplings and brane supersymmetry breaking, Nucl. Phys. B615 (2001) 33–60, [hep-th/0107090]

    2001 arXiv

  272. [280]

    Mourad and A

    J. Mourad and A. Sagnotti,An Update on Brane Supersymmetry Breaking, 1711.11494

    arXiv

  273. [281]

    Dudas and J

    E. Dudas and J. Mourad,D-branes in nontachyonic 0B orientifolds, Nucl. Phys. B 598 (2001) 189–224, [hep-th/0010179]

    2001 arXiv

  274. [282]

    Dudas, J

    E. Dudas, J. Mourad and C. Timirgaziu,Time and space dependent backgrounds from nonsupersymmetric strings, Nucl. Phys. B660 (2003) 3–24, [hep-th/0209176]

    2003 arXiv

  275. [283]

    Dabholkar and J

    A. Dabholkar and J. Park,Strings on orientifolds, Nucl. Phys. B477 (1996) 701–714, [hep-th/9604178]

    1996 arXiv

  276. [284]

    Gukov,K theory, reality, and orientifolds, Commun

    S. Gukov,K theory, reality, and orientifolds, Commun. Math. Phys.210 (2000) 621–639, [hep-th/9901042]

    2000 arXiv

  277. [285]

    Bergman, E

    O. Bergman, E. G. Gimon and P. Horava,Brane transfer operations and T duality of nonBPS states, JHEP 04 (1999) 010, [hep-th/9902160]

    1999 arXiv

  278. [286]

    M. R. Gaberdiel and S. Schafer-Nameki,NonBPS D branes and M theory, JHEP 09 (2001) 028, [hep-th/0108202]

    2001 arXiv

  279. [287]

    Dabholkar and J

    A. Dabholkar and J. Park,An Orientifold of type IIB theory on K3, Nucl. Phys. B 472 (1996) 207–220, [hep-th/9602030]

    1996 arXiv

  280. [288]

    E. G. Gimon and C. V. Johnson,K3 orientifolds, Nucl. Phys. B477 (1996) 715–745, [hep-th/9604129]

    1996 arXiv

  281. [289]

    Horava and E

    P. Horava and E. Witten,Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B475 (1996) 94–114, [hep-th/9603142]

    1996 arXiv

  282. [290]

    Horava and E

    P. Horava and E. Witten,Heterotic and Type I string dynamics from eleven dimensions, Nucl. Phys. B460 (1996) 506–524, [hep-th/9510209]

    1996 arXiv

  283. [291]

    Aharony, Z

    O. Aharony, Z. Komargodski and A. Patir,The Moduli space and M(atrix) theory of 9d N=1 backgrounds of M/string theory, JHEP 05 (2007) 073, [hep-th/0702195]

    2007 arXiv

  284. [292]

    Angelantonj, M

    C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y. S. Stanev,Comments on Gepner models and type I vacua in string theory, Phys. Lett. B387 (1996) 743–749, [hep-th/9607229]

    1996 arXiv

  285. [293]

    Dudas, J

    E. Dudas, J. Mourad and A. Sagnotti,Charged and uncharged D-branes in various string theories, Nucl. Phys. B620 (2002) 109–151, [hep-th/0107081]

    2002 arXiv

  286. [294]

    Sen,SO(32) spinors of type I and other solitons on brane – anti-brane pair, JHEP 09 (1998) 023, [hep-th/9808141]

    A. Sen,SO(32) spinors of type I and other solitons on brane – anti-brane pair, JHEP 09 (1998) 023, [hep-th/9808141]

    1998 arXiv

  287. [295]

    E. G. Gimon and J. Polchinski,Consistency conditions for orientifolds and D-manifolds, Phys. Rev. D54 (1996) 1667–1676, [hep-th/9601038]

    1996 arXiv

  288. [296]

    P. S. Aspinwall,K3 surfaces and string duality, inTheoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, pp. 421–540, 11, 1996.hep-th/9611137

    1996 arXiv

  289. [297]

    D. R. Morrison,On K3 surfaces with large Picard number, Invent Math75 (1984) 105–121

    1984

  290. [298]

    Garbagnati and A

    A. Garbagnati and A. Sarti,Kummer surfaces and K3 surfaces with(Z/2Z)4 symplectic action, Rocky Mountain J.Math.46 (4)(2016) 1141–1205

    2016

  291. [299]

    Gopakumar and S

    R. Gopakumar and S. Mukhi,Orbifold and orientifold compactifications of F - theory 177 and M - theory to six-dimensions and four-dimensions, Nucl. Phys. B479 (1996) 260–284, [hep-th/9607057]

    1996 arXiv

  292. [300]

    Sagnotti,Some properties of open string theories, inInternational Workshop on Supersymmetry and Unification of Fundamental Interactions (SUSY 95), pp

    A. Sagnotti,Some properties of open string theories, inInternational Workshop on Supersymmetry and Unification of Fundamental Interactions (SUSY 95), pp. 473–484, 9, 1995. hep-th/9509080

    1995 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.