Supersymmetry Breaking and alpha'-Corrections to Flux Induced Potentials

Jan Louis; Katrin Becker; Melanie Becker; Michael Haack

REVIEW

Supersymmetry Breaking and alpha'-Corrections to Flux Induced Potentials

Katrin Becker, Melanie Becker, Michael Haack, Jan Louis

High Energy Physics - Theory · Submitted 30 Apr 2002 · 56 references

Pith's verdict: The χ-proportional breaking of no-scale is real and became a standard ingredient; the detailed O(α'³) potential leans on a superpotential non-renormalization argument the paper's own SL(2,Z) discussion undercuts.

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CitationJan Louis, Katrin Becker, Melanie Becker, Michael Haack. "Supersymmetry Breaking and alpha'-Corrections to Flux Induced Potentials." arXiv:hep-th/0204254 (2002). https://pith.science/paper/YYU7NST5

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Two things worth your time here, one solid and one softer than the framing suggests. The solid part: they take the known α'³ correction to the Type IIB hypermultiplet prepotential (Candelas et al., via mirror symmetry), push it through the N=1 orientifold truncation and the Böhm–Günther–Herrmann–Louis field redefinition, and land on a corrected Kähler potential (3.24) with ξ̂ = −χζ(3)/2 · e^{−3φ0/2}. Fed into the standard N=1 potential, that gives a correction ∝ χ which kills no-scale. The appendix is the real work: ξ = −χζ(3)/2 (A.25) and the dilaton shift (A.6) are derived from a careful reduction, including a term (3.4) that does not affect the equations of motion but is needed for the four-dimensional action. That is honest, checkable bookkeeping, and it is why this paper gets cited. The M-theory half is a rederivation of the Becker–Becker vacua from Haack–Louis's potential plus a stability argument from V ≥ 0. Correct, incremental, not the reason to read it. Now the soft spot. The headline — no-scale broken, correction ∝ χ — is carried by the first term of (3.32), δV = −(ξ̂/V̂)V_tree, which follows from the corrected Newton constant (3.35) and needs no assumption about W. That part is robust. The second term (3.36) depends on D_τ W and hence on W = ∫G_3∧Ω being uncorrected. Their argument for that is SL(2,Z) acting as a Kähler transformation on K. But two paragraphs earlier they say the dilaton background (3.14) is not SL(2,Z)-invariant — only c = 0 survives — and at ξ ≠ 0 the combination V̂ + ξ̂/2 does not scale as |cτ+d|^{−2}, so (3.30) fails at exactly the order being computed. The unbroken l-shift alone permits arbitrary e^{−φ0} dependence in W. So the non-renormalization argument does not close at O(α'³). The authors half-acknowledge this: they note the second term lacks a complete ten-dimensional origin and that reducing (3.38) gives the wrong factor and extra (2,1)-form terms. So it is a known-soft term, not a hidden one — but the symmetry argument as written is doing more work than it can bear. Verdict: the qualitative result stands and is worth citing; the detailed (3.31) is provisional. Send it out.

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Major objections (2)

[§3, eqs. (3.31)-(3.32) and the paragraph following (3.30)] The argument that W = ∫G_3∧Ω receives no α'³ corrections relies on SL(2,Z) acting as a Kähler transformation (3.30). At ξ≠0, however, the corrected Kähler potential (3.24) contains ξ̂ = ξe^{-3φ0/2}, which under τ → (aτ+b)/(cτ+d) scales as |cτ+d|^{-3}, so V̂ + ξ̂/2 does not scale as |cτ+d|^{-2} and (3.30) fails. The authors themselves note just before (3.26) that the background (3.14) is not SL(2,Z)-invariant and that only the c=0 subgroup survives; the unbroken shift symmetry of l alone does not force the combination F_3 - τH_3. This matters because the |W|² term in (3.32) is what lifts the radial modulus at the minimum, since the first term vanishes when V_tree = 0. The authors acknowledge the second term's incomplete ten-dimensional origin, but the symmetry argument should be re-examined or the limitation stated more explicitly.
[§3, eq. (3.32)] The logical structure of the correction deserves clarification. The first term δV = -(ξ̂/V̂)V_tree vanishes at the tree-level minimum V_tree = 0, so it does not by itself lift the radial modulus; the physical claim that supersymmetry breaking via W ≠ 0 induces a non-vanishing potential rests on the second term, which depends on the W non-renormalization assumption discussed above. The abstract and conclusions should distinguish which part of the result is robust (the χ-proportional correction to the potential) from which part depends on that assumption.

Minor objections (7)

[Abstract] The abstract says α'-corrections 'may indeed lead to a stabilization of the radial modulus', but the body shows a runaway at O(α'³) and only conjectures stabilization at higher order. The abstract should be more precise about this distinction.
[§3, eq. (3.31)] The potential has poles at V̂ = ξ̂ and V̂ = -2ξ̂. For χ > 0, ξ < 0, so the pole at V̂ = |ξ̂|/2 lies within the regime where the α' expansion might be marginally valid. The paper should state the regime of validity V >> |ξ| and discuss the behaviour near the poles.
[§3, eq. (3.20)] The first term 2e^{φ0/2}ξ̂ in the truncated Lagrangian is a potential term; its origin and its relation to the scalar potential (3.31) should be clarified.
[§3, eq. (3.24)] The notation ξ̂ in the first line versus ξe^{-3φ0/2} in the second line should be harmonized, and the definition of ξ̂ should be stated once.
[§3, paragraph before (3.26)] The statement that 'only the subgroup of (3.25) with c = 0 leaves l constant' is imprecise: c = 0 with a = d = 1 shifts l rather than leaving it constant. The intended meaning (that the constant-l background is mapped to a constant-l background) should be stated explicitly.
[§3, discussion after (3.36)] The claim that a term ∼ G Ḡ R³ 'is not to be expected from an analysis using the linearized Type IIB supersymmetry' is a statement about the literature and should be supported with a reference or softened.
[§3, truncation (3.13)] The paper states that consistency of the truncation with [43] was checked, but the details are not shown. It would be helpful to display the check or at least the structure of the truncation, even briefly.

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The paper

The paper claims

The paper argues that once $O(alpha'^3)$ string corrections are included, the classical cancellation of vacuum energy in flux compactifications of Type IIB string theory on Calabi-Yau threefolds fails, and the resulting potential is tied to

The reading

The paper has two aims. First, it re-derives the non-supersymmetric M-theory vacua of an earlier paper by minimizing an explicit three-dimensional scalar potential, and shows that those vacua sit at the bottom of a potential that is non-negative by construction, so they are classically stable and carry zero cosmological constant. Second, it asks what happens to the no-scale property of flux potentials once higher-derivative string corrections are included: in Type IIB compactifications on Calabi-Yau threefolds with three-form flux and localized sources, the classical potential is independent of the overall volume, so supersymmetry can be broken by a $(0,3)$ flux without generating vacuum energy. The authors show that the $O(alpha'^3)$ correction to the prepotential, transmitted through mirror symmetry and the c-map into a correction of the $N=1$ Kähler potential, produces a scalar potential that depends on the volume and is proportional to the Euler number $chi$ of the internal manifold. The consequence they draw is that no-scale structure does not survive quantum corrections, supersymmetry breaking by flux now costs energy, and the radial modulus, while still not stabilized at this order, is pushed by a potential that could be stabilized by further corrections.

What carries the argument

The load-bearing device is the perturbatively corrected prepotential of the Kähler moduli, $F(X) = (i/3!)κ_{abc}X^aX^bX^c/X^0 + (X^0)^2ξ$ with $ξ = -χζ(3)/2$, obtained from mirror symmetry and identified with the $alpha'$ corrections to the hypermultiplet moduli space. Because the hypermultiplet metric is fixed by the prepotential through the c-map, the correction can be transported into Type IIB variables via a known field-basis map, truncated to an $N=1$ subsector by projecting out the fields from the antisymmetric two-forms, and then assembled into an $N=1$ Kähler potential whose second derivatives give the corrected potential. A second piece of machinery is the auxiliary term $∼(∇^2φ)Q$ with $Q$ the six-dimensional Euler integrand, which vanishes on-shell at $O(alpha'^3)$ but is required to obtain the correct four-dimensional effective action and the correct relation $e^{-2φ_4} = e^{-2φ_0}(V + ξ/2)$ between the four- and ten-dimensional dilatons. The argument that the superpotential $W = ∫G_{(3)}∧Ω$ receives no $alpha'$ corrections rests on the Peccei-Quinn shift symmetry of the Kähler moduli and on the dilaton's shift symmetry being a subgroup of $SL(2,ℤ)$.

Extended reading notes

Core claim

The central claim is that in Type IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources, the $alpha'^3$ corrections generate a correction to the four-dimensional supergravity potential proportional to the Euler number of the internal manifold, which spoils the no-scale structure of the classical potential. Concretely, the corrected Kähler potential is $K = -ln[-i(τ-τ̄)] - 2ln(-i(T^a-T̄^a)v̂_a + ξ(-i(τ-τ̄))^{3/2}) - ln[-i∫Ω∧Ω̄]$ with $ξ = -χζ(3)/2$, and expanding the $N=1$ potential $V = e^K(G^{-1 IJ}D_IW D̄_JW̄ - 3|W|^2)/2κ_{10}^2$ gives $δV = -(ξ̂/V̂)V_{tree} + (3/8)e^{K^{(0)}}κ^{-2}ξ̂V̂|W + (τ-τ̄)D̃_τW|^2$. The $|W|^2$ term no longer cancels, so breaking supersymmetry via $W ≠ 0$ no longer yields vanishing vacuum energy, and the potential acquires a non-trivial dependence on the radial mode. For manifolds with $χ = 0$ the corrections vanish and the classical behaviour is retained. The authors also re-derive the non-supersymmetric M-theory flux vacua from the scalar potential of an earlier reduction, showing that a flux of the form $F = F_{4,0}+F_{0,4}+F_{0,0}J∧J$ satisfies $D_αW = D_AŴ = 0$ and hence gives a stable, zero-cosmological-constant vacuum that breaks supersymmetry.

Load-bearing premise

The load-bearing premise is that the mirror-symmetry-derived correction to the prepotential survives the truncation to an $N=1$ subsector and the change of field variables, so that the corrected Kähler potential used here really is the Kähler potential of the four-dimensional theory.

Editorial extensions

If this is right

The non-supersymmetric M-theory compactifications with flux $F = F_{4,0}+F_{0,4}+F_{0,0}J∧J$ have a vanishing three-dimensional cosmological constant and are classically stable, since the potential is non-negative and these configurations sit at its minimum.
In Type IIB, breaking supersymmetry with a non-vanishing $W$ no longer gives zero vacuum energy once $O(alpha'^3)$ corrections are kept, because the $|W|^2$ term survives in the potential.
Compactifications on internal manifolds with vanishing Euler number retain the no-scale structure and the classical stability at this order, so the correction is a sharp function of internal topology.
At $O(alpha'^3)$ the radial modulus is still not stabilized: the correction produces a runaway rather than a minimum, so stabilization would have to come from corrections with a different power of the volume.
If such higher corrections do stabilize the modulus, a cosmological constant would be generated at higher order, and the authors speculate that its sign could be positive, giving de Sitter space.
The correction is suppressed in the large-volume limit, as is the effect of the warp factor from localized sources, so the result is under control in the same regime where the classical treatment is valid.

Reading between the lines

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

The dependence on the Euler number acts as a selection rule: two compactifications with identical flux and volume but different internal topology should differ in vacuum energy at this order, which is a sharper statement than 'quantum corrections matter' and is in principle a discriminating check.
The authors note that reducing the ten-dimensional $H^2$ term with the corrected dilaton does not reproduce the coefficient of the second correction term, and that extra $(2,1)$-form contributions would be expected. That mismatch is a quantitative handle: it constrains the size of any $G\bar{G}R^3$ coupling in ten dimensions, which the authors flag as not expected from linearized supersymmetry.
Because the correction vanishes for $χ = 0$, the mechanism cannot operate in toroidal or otherwise Euler-number-free compactifications; any claim of modulus stabilization from this effect alone is confined to topologically non-trivial internal spaces.
The auxiliary total-derivative term $(∇^2φ)Q$ is invisible to the equations of motion but changes the four-dimensional action. This suggests that other such terms, easily dropped in a naive reduction, may be needed elsewhere in the same programme before the corrected potential can be trusted beyond leading order.

Original abstract

We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory. Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant. We show that in the context of Type IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources alpha'-corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential. This indicates that alpha'-corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory. Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant. We show that in the context of Type IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources alpha'-corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential. This indicates that alpha'-corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory.	contribution 0.85	0.95	0.07	asserted 1.00
s1	Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant.	result 1.00	0.75	0.11	asserted 1.00
s2	We show that in the context of Type IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources alpha'-corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential.	result 0.80	0.88	0.47	asserted 1.00
s3	This indicates that alpha'-corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications.	interpretation 1.00	0.57	0.34	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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references and citing sentences
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levels run

P abstract

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References

Works cited (56)

[17]

K. Becker and M. Becker, “Supersymmetry Breaking, M-Theory and Fluxes”, JHEP 0107:038 (2001), hep-th/0107044

View on Pith Pith review arXiv 2001
[21]

M. Haack and J. Louis, “ M-Theory Compactiﬁed on Calabi-Yau Fourfolds with Back- ground Flux”, Phys. Lett. B507 (2001) 296, hep-th/0103068

View on Pith Pith review arXiv 2001
[32]

S. Ferrara and S. Sabharwal, “Quaternionic Manifolds f or Type II Superstring Vacua of Calabi-Yau Spaces”, Nucl. Phys. B332 (1990) 317

View on Pith 1990
[38]

R. B¨ ohm, H. G¨ unther, C. Herrmann and J. Louis, “Compac tiﬁcation of Type IIB String Theory on Calabi-Yau Threefolds”, Nucl. Phys. B569 (2000) 229, hep- th/9908007

View on Pith 2000
[1]

M. Dine, R. Rohm, N. Seiberg and E. Witten, “Gluino Conden sation in Superstring Models”, Phys. Lett. B156 (1985) 55

View on Pith 1985
[2]

J. P. Derendinger, L. E. Ibanez and H. P. Nilles, “On The Lo w-Energy D = 4, N=1 Supergravity Theory Extracted from the D = 10, N=1 Superstri ng”, Phys. Lett. B155 (1985) 65

View on Pith 1985
[3]

R. Rohm and E. Witten, “The Antisymmetric Tensor Field in Superstring Theory”, Ann. Phys. 170 (1986) 454

View on Pith 1986
[4]

For a recent review see, for example, H. P. Nilles, “Hidde n Sector Supergravity Break- down”, Nucl. Phys. Proc. Suppl. 101 (2001) 237, hep-ph/0106063

View on Pith Pith review arXiv 2001
[5]

S. B. Giddings, S. Kachru and J. Polchinski, “Hierarchie s from Fluxes in String Com- pactiﬁcations”, hep-th/0105097

View on Pith Pith review arXiv
[6]

S. Kachru, M. Schulz and S. Trivedi, “Moduli Stabilizati on from Fluxes in a Simple IIB Orientifold”, hep-th/0201028

View on Pith Pith review arXiv
[7]

A. R. Frey and J. Polchinski, “ N = 3 Warped Compactiﬁcations”, hep-th/0201029

View on Pith Pith review arXiv
[8]

C. Angelantonj and A. Sagnotti, “Open strings”, hep-th/ 0204089

View on Pith
[9]

M. Grana and J. Polchinski, “Supersymmetric Three-Form Flux Perturbations on AdS(5)”, Phys. Rev. D63 (2001) 026001, hep-th/0009211

View on Pith Pith review arXiv 2001
[10]

S.S. Gubser, “Supersymmetry and F -Theory Realization of the Deformed Conifold with Three-Form Flux”, hep-th/0010010

View on Pith Pith review arXiv
[11]

J. Michelson, “Compactiﬁcations of Type IIB Strings to Four Dimensions with Non- Trivial Classical Potential”, Nucl. Phys. B495 (1997) 127, hep-th/9610151

View on Pith Pith review arXiv 1997
[12]

T.R. Taylor and C. Vafa, “R-R Flux on Calabi-Yau and Part ial Supersymmetry Break- ing”, Phys. Lett. B474 (2000) 130, hep-th/9912152

View on Pith Pith review arXiv 2000
[13]

P. Mayr, “On Supersymmetry Breaking in String Theory an d its Realization in Brane Worlds”, Nucl. Phys. B593 (2001) 99, hep-th/0003198

View on Pith Pith review arXiv 2001
[14]

G. Dall’Agata, “Type IIB Supergravity Compactiﬁed on a Calabi-Yau Manifold with H-Fluxes”, JHEP 0111:005 (2001), hep-th/0107264

View on Pith Pith review arXiv 2001
[15]

J. Louis and A. Micu, “Type II Theories Compactiﬁed on Ca labi-Yau Threefolds in the Presence of Background Fluxes”, hep-th/0202168

View on Pith Pith review arXiv
[16]

G. Curio, A. Klemm, D. L¨ ust and S. Theisen, “On the Vacuu m Structure of Type II String Compactiﬁcations on Calabi-Yau Spaces with H-Flu xes”, Nucl. Phys. B609 (2001) 3, hep-th/0012213

View on Pith Pith review arXiv 2001
[18]

K. Becker and M. Becker, “ M-Theory on Eight-Manifolds”, Nucl. Phys. B477 (1996) 155 hep-th/9605053. 24

View on Pith Pith review arXiv 1996
[19]

S. Gukov, C. Vafa and E. Witten, “CFT’s from Calabi-Yau F our-Folds”, Nucl. Phys. B484 (2000) 69, hep-th/9906070

View on Pith Pith review arXiv 2000
[20]

M. Haack and J. Louis, “Duality in Heterotic Vacua with F our Supercharges”, Nucl. Phys. B575 (2000) 107, hep-th/9912181

View on Pith Pith review arXiv 2000
[22]

M. Haack, J. Louis and M. Marquart, “Type IIA and Heterot ic String Vacua in D = 2”, Nucl. Phys. B598 (2001) 30, hep-th/0011075

View on Pith Pith review arXiv 2001
[23]

S. Gukov and M. Haack, “IIA String Theory on Calabi-Yau F ourfolds with Background Fluxes”, hep-th/0203267

View on Pith Pith review arXiv
[24]

C. Beasley and E. Witten, “A Note on Fluxes and Superpote ntials in M-theory Com- pactiﬁcations on Manifolds of G2 Holonomy”, hep-th/0203061

View on Pith Pith review arXiv
[25]

K. Dasgupta, G. Rajesh and S. Sethi, “ M-Theory, Orientifolds and G-Flux”, JHEP 9908:023 (1999), hep-th/9908088

View on Pith Pith review arXiv 1999
[26]

E. J. Cremmer, B. Julia and L. Scherk, “Supergravity The ory in Eleven Dimensions”, Phys. Lett. B5 (1978) 409

View on Pith 1978
[27]

A. Kehagias and H. Partouche, “The Exact Quartic Eﬀecti ve Action for the Type IIB Superstring”, Phys. Lett. B422 (1998) 109, hep-th/9710023

View on Pith Pith review arXiv 1998
[28]

K. Peeters, P. Vanhove and A. Westerberg, “Supersymmet ric Higher Derivative Actions in Ten Dimensions and Eleven Dimensions, the Associ ated Superalgebras and their Formulation in Superspace”, Class. Quantum Grav. 18 (2001) 843, hep- th/0010167

View on Pith 2001
[29]

S. Frolov, I. Klebanov and A. Tseytlin, “String Correct ions to the Holographic RG Flow of Supersymmetric SU (N ) ×SU (N +M ) Gauge Theory”, Nucl. Phys. B620 (2002) 84, hep-th/0108106

View on Pith Pith review arXiv 2002
[30]

K. Peeters, P. Vanhove and A. Westerberg, “Chiral Split ting and World Sheet Grav- itinos in Higher Derivative String Amplitudes”, hep-th/01 12157

View on Pith
[31]

M.B. Green, “Interconnections Between Type II Superst rings, M-theory and N = 4 Supersymmetric Yang-Mills”, hep-th/9903124

View on Pith Pith review arXiv
[33]

I. Antoniadis, S. Ferrara, R. Minasian and K. S. Narain, “R4 Couplings in M and Type II Theories on Calabi-Yau Spaces”, Nucl. Phys. B507 (1997) 571, hep-th/9707013

View on Pith Pith review arXiv 1997
[34]

D. Gross and E. Witten, “Superstring Modiﬁcation of Ein stein Equations”, Nucl. Phys. B277 (1986) 1

View on Pith 1986
[35]

M.D. Freeman and C.N. Pope, “Beta-Functions and Supers tring Compactiﬁcations”, Phys. Lett. B174 (1986) 48. 25

View on Pith 1986
[36]

M. T. Grisaru, A. E. M. van de Ven and D. Zanon, “Four-Loop Divergences for the N = 1 Supersymmetric Non-Linear Sigma-Model in Two Dimension s”, Nucl. Phys. B277 (1986) 409

View on Pith 1986
[37]

P. Candelas, X. C. De La Ossa, P. S. Green and L. Parkes, “A Pair of Calabi-Yau Manifolds as an Exactly Soluble Superconformal Field Theor y”, Nucl. Phys. B359 (1991) 21

View on Pith 1991
[39]

M. Bodner and A. C. Cadavid, “Dimensional Reduction of t he Type IIB Supergravity and Exceptional Quaternionic Manifolds”, Class. Quantum Grav. 7 (1990) 829

View on Pith 1990
[40]

C.W. Misner, K.S. Thorne and J.A. Wheeler, “Gravitatio n”, Freeman, San Francisco (1973)

View on Pith 1973
[41]

M.T. Grisaru, A.E. van de Ven and D. Zanon, “Four Loop Bet a Function for fhe N = 1 and N = 2 Supersymmetric Nonlinear Sigma Model in Two Dimensions” , Phys. Lett. B173 (1986) 423

View on Pith 1986
[42]

M. T. Grisaru, A.E.M. van de Ven and D. Zanon, “Two-dimen sional Supersymmetric Sigma Models on Ricci Flat K¨ ahler Manifolds are not Finite” , Nucl. Phys. B277 (1986) 388

View on Pith 1986
[43]

L. Andrianopoli, R. D’Auria and S. Ferrara, “Supersymm etry Reduction of N - Extended Supergravities in Four Dimensions”, JHEP 0203:025 (2002), hep-th/0110277

View on Pith Pith review arXiv 2002
[44]

L. Andrianopoli, R. D’Auria and S. Ferrara, “Consisten t Reduction of N = 2 → N = 1 Four Dimensional Supergravity Coupled to Matter”, Nucl. Phys. B628 (2002) 387, hep-th/0112192

View on Pith Pith review arXiv 2002
[45]

A. Sen, “Central Charge of the Virasoro Algebra for Supe rsymmetric Sigma Models on Calabi-Yau Manifolds”, Phys. Lett. B178 (1986) 370

View on Pith 1986
[46]

M.D. Freeman, C.N. Pope, M.F. Sohnius and K.S. Stelle, “ Higher Order σ-Model Counterterms and the Eﬀective Action for Superstrings”, Phys. Lett. B178 (1986) 199

View on Pith 1986
[47]

P. Candelas, M.D. Freeman, C.N. Pope, M.F. Sohnius and K .S. Stelle, “Higher Order Corrections to Supersymmetry and Compactiﬁcations of the H eterotic String”, Phys. Lett. B177 (1986) 341

View on Pith 1986
[48]

J. Polchinski, “String Theory”, 2 vols., Cambridge University Press (1998)

View on Pith 1998
[49]

E. Witten, “New Issues in Manifolds of SU (3) Holonomy”, Nucl. Phys. B268 (1986) 79

View on Pith 1986
[50]

P.S. Howe and P.C. West, “The Complete N = 2, D = 10 Supergravity”, Nucl. Phys. B238 (1984) 181

View on Pith 1984
[51]

A. A. Tseytlin, “ R4 Terms in 11 Dimensions and Conformal Anomaly of (2 , 0) The- ory”, Nucl. Phys. B584 (2000) 233, hep-th/0005072. 26

View on Pith Pith review arXiv 2000
[52]

E. J. Cremmer and S. Ferrara, “Formulation of Eleven-Di mensional Supergravity in Superspace”, Phys. Lett. B91 (1980) 61; L. Brink and P. Howe, “Eleven-Dimensional Supergravity on the Mass-Shell in Superspace”, Phys. Lett. B91 (1980) 384

View on Pith 1980
[53]

A. Strominger, “Loop Corrections to the Universal Hype rmultiplet”, Phys. Lett. B421 (1998) 139, hep-th/9706195

View on Pith Pith review arXiv 1998
[54]

T. Banks, “Cosmological Breaking of Supersymmetry? or Little Lambda Goes Back to the Future 2”, hep-th/0007146

View on Pith Pith review arXiv
[55]

M. T. Grisaru and D. Zanon, “Sigma-Model Superstring Co rrections to the Einstein Hilbert Action”, Phys. Lett. B177 (1986) 347

View on Pith 1986
[56]

Q.H. Park and D. Zanon, “More on Sigma Model Beta Functio ns and Low-Energy Eﬀective Actions”, Phys. Rev. D35 (1987) 4038. 27

View on Pith 1987

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Showing 60 of 110 Pith papers that cite this

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de Sitter Vacua in String Theory
hep-th 2003-01 conditional novelty 9.0 of 10

Type IIB flux compactification, plus a non-perturbative superpotential, plus a warped anti-D3 uplift, yields a metastable de Sitter vacuum with all moduli fixed and a lifetime far exceeding 10^10 years.
Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications
hep-th 2005-02 accept novelty 8.0 of 10

A quantum correction to the internal geometry, competing with non-perturbative effects, produces a tachyon-free AdS minimum at exponentially large volume in type IIB flux compactifications, with a flux-independent gra...
New Type IIB Poly-instanton Effects and Axion Quintessence
hep-th 2026-07 conditional novelty 7.0 of 10

Deformation divisors can generate poly-instanton superpotential terms in type IIB Calabi-Yau orientifolds when O3-planes lie on the E3-brane, with explicit CY examples and an axion-quintessence construction matching t...
Towards the Non-Perturbative Completion of 4d N=1 Effective Theories of Gravity
hep-th 2025-10 conditional novelty 7.0 of 10

Small-volume regimes of flop curves in 4d N=1 F-theory require non-perturbative states—blow-up moduli and D3-string excitations—to complete the locally enhanced N=2 spectrum.
Cosmic superstrings in large volume compactifications: PTAs, LISA and time-varying tension
astro-ph.CO 2025-04 conditional novelty 7.0 of 10

Cosmic superstrings with a time-varying tension in large-volume string compactifications generically predict a LISA-band spectral drop and a high-frequency f^4 boost, encoding the mass and decay of the volume modulus.

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Chiral global embedding of Fibre Inflation with $\overline{\rm D3}$ uplift
hep-th 2024-12 conditional novelty 7.0 of 10

Explicit construction of a chiral global embedding of Fibre Inflation with anti-D3 uplift on an h^{1,1}=4 K3-fibered Calabi-Yau, using magnetised D7-branes, a Whitney brane, and O3-planes at a conifold tip, with viabl...
LVS de Sitter Vacua are probably in the Swampland
hep-th 2022-01 conditional novelty 7.0 of 10

Corrections to the LARGE-volume scenario of type IIB string theory appear unsuppressed in the moduli vevs, vacuum energy, and masses, suggesting that dS vacua in this scenario are uncontrolled.
SUSY Breaking in Local String/F-Theory Models
hep-th 2009-06 conditional novelty 7.0 of 10

Gravity-mediated soft terms in LARGE-volume local string models are suppressed by Ms/MP relative to the gravitino mass, so TeV soft masses imply a gravitino above 10^8 GeV and a volume of order 10^6-10^7.
Fibre Inflation: Observable Gravity Waves from IIB String Compactifications
hep-th 2008-08 conditional novelty 7.0 of 10

A K3-fibre Kähler modulus in a large-volume type IIB compactification drives large-field inflation with a parameter-free relation r ≈ 6(ns-1)², predicting r ≈ 0.005 and ns ≈ 0.970.
Towards an Explicit Model of D-brane Inflation
hep-th 2007-06 conditional novelty 7.0 of 10

For the Kuperstein D7 embedding, the full D3-brane inflaton potential including moduli-stabilization corrections can be fine-tuned to support slow-roll inflation near an inflection point, while ACR embeddings admit no...
Generalized N=1 Orientifold Compactifications and the Hitchin functionals
hep-th 2006-02 conditional novelty 7.0 of 10

The paper derives N=1 Kähler potentials and superpotentials for type II orientifolds on SU(3)-structure manifolds and proposes generalized half-flat manifolds as mirrors of Calabi-Yau compactifications with NS-NS flux.
The QCD Axion and Moduli Stabilisation
hep-th 2006-02 conditional novelty 7.0 of 10

A clean supergravity no-go theorem forbids supersymmetric moduli stabilization with a flat QCD axion, and a large-volume construction gives f_a approximately the geometric mean of the Planck and SUSY-breaking scales.
Large-Volume Flux Compactifications: Moduli Spectrum and D3/D7 Soft Supersymmetry Breaking
hep-th 2005-05 conditional novelty 7.0 of 10

In Calabi-Yau flux vacua with exponentially large volume, moduli masses and D3/D7 soft supersymmetry-breaking terms follow a hierarchy set by inverse powers of the volume, dominated by the large Kahler modulus F-term.
Mirror Symmetry in Generalized Calabi-Yau Compactifications
hep-th 2002-11 conditional novelty 7.0 of 10

Type IIB on a Calabi-Yau threefold with electric NS three-form flux is mirror to type IIA on a half-flat SU(3)-structure manifold, and the two four-dimensional effective actions agree.
$\alpha'$-Bootstrap
hep-th 2026-07 conditional novelty 6.5 of 10

An infinite-dimensional algebraic structure on a megaspace yields recursive, T-duality-covariant NS-NS α' and α'^{2} corrections matching known bosonic and heterotic results up to field redefinitions.
Axionic Quintessence in Heterotic String Theory
hep-th 2026-10 conditional novelty 6.0 of 10

A heterotic string-derived axionic quintessence model is explored, showing that aligned instantons can produce an ultralight axion with f~0.4M_p, but the required instanton selection and moduli stabilization are not y...
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hep-th 2026-08 conditional novelty 6.0 of 10

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On Calabi-Yau Threefolds For Unified LVS Inflation
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A database scan identifies 2+14+45 Calabi-Yau threefolds with specified fibration and divisor structures that unify three LVS Kähler moduli inflation models.
Quantum obstructions for $N=1$ infinite distance limits -- Part I: $g_s$ obstructions
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Non-perturbative g_s corrections obstruct perturbative Type IIB descriptions and can remove classical infinite distance degenerations in asymptotic regions of the complex structure moduli space.
The String Theory Photoverse
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Massless string-theory hidden photons acquire dimension-six dipole couplings to SM fermions with suppression scale Λ = αM_s, converting dipole measurements into constraints on the string scale.
Towards a Heterotic Axiverse
hep-th 2025-09 conditional novelty 6.0 of 10

Generic heterotic axions are heavier than in type IIB; the Strong CP problem is typically unsolved, and a light fuzzy dark matter axion requires a no-gaugino-condensation anisotropic fibred Calabi-Yau.
Type IIB at eight derivatives: Five-Point Axio-Dilaton Couplings
hep-th 2025-07 conditional novelty 6.0 of 10

The complete five-point, eight-derivative effective action of Type IIB in the gravity plus axio-dilaton sector is derived, with identical tree-level and one-loop kinematics and full SL(2,Z) modular completion.
Perturbative K\"ahler Moduli Inflation
hep-th 2025-06 reject novelty 6.0 of 10

Two classes of slow-roll inflation potentials, V0(1+C1 φ^(2/3)) and V0(1-C2 φ^(-2/3)), are derived from perturbative Kähler moduli stabilization and give r below 10^-2 and 10^-8.
Superheavy Dark Matter from the String Theory Axiverse
hep-th 2025-04 conditional novelty 6.0 of 10

Heavy axions from a simple string-theory compactification can be produced in large numbers by gravitational particle production at the end of inflation and can account for all dark matter, provided they remain stable ...
Preheating Axions in String Cosmology
hep-th 2024-11 conditional novelty 6.0 of 10

Preheating of closed-string axions in fibre inflation can overproduce dark matter, yielding new upper bounds on the axion mass and constraints on model parameters.
Fuzzy Dark Matter Candidates from String Theory
hep-th 2021-10 conditional novelty 6.0 of 10

In type IIB flux compactifications only C4 volume axions, C2 axions and thraxions can supply a large fuzzy dark matter fraction, and only by mildly violating the Sf < M_P bound.
Small Cosmological Constants in String Theory
hep-th 2021-07 conditional novelty 6.0 of 10

Explicit type IIB orientifolds with quantized fluxes admit supersymmetric AdS4 vacua in which all closed-string moduli are stabilized and the cosmological constant is below 10^-123 in Planck units.
The Standard Model Quiver in de Sitter String Compactifications
hep-th 2021-06 conditional novelty 6.0 of 10

An explicit type IIB Calabi-Yau compactification is constructed in which D3-branes at a dP5 singularity give a three-family left-right symmetric model, with closed-string moduli stabilised in a de Sitter minimum.
Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture
hep-th 2020-10 conditional novelty 6.0 of 10

Leading α'^2 corrections obstruct F-theory infinite distance limits in which an emergent string would lie parametrically below the Kaluza-Klein scale, and 1-loop threshold corrections plus mass renormalization modify ...
Control issues of KKLT
hep-th 2020-09 conditional novelty 6.0 of 10

KKLT-compatible flux compactifications generically drive the warp factor negative over a large part of the Calabi-Yau, producing singularities that break the 10d supergravity control the construction relies on.
UV Shadows in EFTs: Accidental Symmetries, Robustness and No-Scale Supergravity
hep-th 2020-06 conditional novelty 6.0 of 10

Accidental scaling symmetries of ten-dimensional supergravity, combined with supersymmetry and axionic shifts, fix the all-orders form of the four-dimensional Kähler potential and explain why no-scale structure is ubi...
A Systematic Approach to K\"ahler Moduli Stabilisation
hep-th 2020-05 conditional novelty 6.0 of 10

Working in 2-cycle volume moduli plus a hybrid genetic/clustering/amoeba search reproduces known KKLT and LVS vacua and yields new LVS minima on Calabi-Yau threefolds without a diagonal del Pezzo divisor.
Logarithmic loop corrections, moduli stabilisation and de Sitter vacua in string theory
hep-th 2019-09 conditional novelty 6.0 of 10

A logarithmic loop correction to the 4d Planck mass in type IIB compactifications is computed and used to stabilize Kähler moduli in a de Sitter vacuum at large volume and weak coupling.
Quantum Corrections and the de Sitter Swampland Conjecture
hep-th 2018-08 conditional novelty 6.0 of 10

Exact four-dimensional de Sitter in dimensionally reduced M-theory requires an infinite, hierarchyless tower of quantum corrections, so no effective field theory description exists, though quasi-de Sitter with mild ti...
The de Sitter swampland conjecture and supersymmetric AdS vacua
hep-th 2018-08 accept novelty 6.0 of 10

In single-modulus flux compactifications, the de Sitter swampland conjecture implies the absence of supersymmetric AdS vacua, so the standard one-modulus KKLT AdS solution would falsify it.
Primordial Black Holes from String Inflation
hep-th 2018-03 conditional novelty 6.0 of 10

A type IIB fibre inflation model with a tuned near-inflection point produces a power-spectrum spike large enough to seed primordial black holes at 10^-14 solar masses, potentially accounting for all dark matter.
A Geometrical Upper Bound on the Inflaton Range
hep-th 2018-01 conditional novelty 6.0 of 10

In type IIB LVS string models with three Kähler moduli, the reduced moduli space of flat directions is compact, bounding the inflaton field range by a logarithm of the Calabi-Yau volume.
Supersymmetry Breaking by Fluxes
hep-th 2017-09 conditional novelty 6.0 of 10

Supersymmetry-breaking flux backgrounds in string theory are argued to be generically time-dependent rolling solutions rather than static vacua, which would invalidate standard de Sitter landscape constructions.
Chiral Global Embedding of Fibre Inflation Models
hep-th 2017-09 conditional novelty 6.0 of 10

A Calabi-Yau orientifold with four Kähler moduli, a suitable D7-brane and flux choice, and one Fayet-Iliopoulos term reduces to a chiral fibre-inflation model whose Kähler cone bounds tightly limit the inflaton range.
Towards de Sitter from 10D
hep-th 2017-07 conditional novelty 6.0 of 10

The single-condensate KKLT vacuum cannot be uplifted to de Sitter because the 10D on-shell potential stays negative under the anti-brane backreaction, while racetrack stabilization can evade this.
Global Orientifolded Quivers with Inflation
hep-th 2017-06 conditional novelty 6.0 of 10

An explicit type IIB Calabi-Yau orientifold is built in which fractional D3 branes give a chiral quiver sector, a T-brane hidden sector stabilises all closed-string moduli in de Sitter, and a del Pezzo divisor drives ...
Global Embedding of Fibre Inflation Models
hep-th 2016-11 conditional novelty 6.0 of 10

An explicit toric Calabi-Yau orientifold with h^{1,1}=3, a K3 fibration and a shrinkable del Pezzo divisor is shown to reproduce the fibre inflation potential from string loop corrections.
$\alpha'$ Inflation: Moduli Stabilisation and Observable Tensors from Higher Derivatives
hep-th 2016-07 conditional novelty 6.0 of 10

Higher-derivative alpha-prime F4 corrections lift the flat directions left over in type IIB Large Volume Scenario compactifications, and combined with winding loop corrections they drive inflation with spectral index ...
Moduli Vacuum Misalignment and Precise Predictions in String Inflation
hep-th 2016-04 conditional novelty 6.0 of 10

In Kahler moduli inflation, the volume modulus is displaced by roughly 0.1 to 1 Planck units during inflation, and its late decay lowers the required number of e-foldings from about 50 to about 45, shifting the spectr...
F-theory at order $\alpha'^3$
hep-th 2015-06 conditional novelty 6.0 of 10

A twelve-dimensional repackaging of type IIB eight-derivative couplings yields a new, genuinely N=1 alpha'^3 correction to the four-dimensional effective action of F-theory on elliptically fibered Calabi-Yau fourfolds.
Higher-Derivative Supergravity and Moduli Stabilization
hep-th 2015-05 conditional novelty 6.0 of 10

Higher-derivative (alpha')^3 corrections to type IIB flux compactifications generate a scalar potential that stabilizes all Kahler moduli of Calabi-Yau orientifolds with positive Euler number, provided the correction'...
Planckian Axions in String Theory
hep-th 2014-12 conditional novelty 6.0 of 10

The diameter of the axion fundamental domain in the 51-modulus DDFGK Calabi-Yau vacuum is computed to be about 1.1 Planck masses, and random-matrix arguments suggest it scales as N times the largest decay constant.
Tuning and Backreaction in F-term Axion Monodromy Inflation
hep-th 2014-11 conditional novelty 6.0 of 10

A no-go theorem rules out weakly coupled type IIB orientifold realisations of F-term axion monodromy inflation, while Calabi-Yau fourfolds evade it and appear to leave a workable flux landscape.
D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation
hep-th 2014-05 conditional novelty 6.0 of 10

The paper derives a corrected Type IIB D7-brane superpotential, shows the extended no-scale cancellation survives a light brane modulus, and argues fluxbrane inflation can be made parametrically consistent, though onl...
D7-Brane Chaotic Inflation
hep-th 2014-04 conditional novelty 6.0 of 10

D7-brane position moduli in Type IIB orientifolds can serve as large-field inflatons, with a mirror-symmetry shift symmetry and flux-induced monodromy, provided the flux coefficients can be tuned small.
N-flation with Hierarchically Light Axions in String Compactifications
hep-th 2014-01 conditional novelty 6.0 of 10

A LARGE Volume Scenario compactification with N large four-cycles yields N hierarchically light axions whose collective motion reproduces N-flation, at the cost of about 10^5 Kahler moduli and GUT-scale supersymmetry.
Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter
hep-th 2013-11 conditional novelty 6.0 of 10

An explicit fluxed type IIB orientifold with chiral matter at a dP6 singularity has every closed string modulus stabilised, giving a de Sitter vacuum with TeV-scale soft terms.
Heterotic Moduli Stabilisation
hep-th 2013-04 conditional novelty 6.0 of 10

Alpha-prime corrections to the Kähler potential yield stable near-Minkowski heterotic vacua at volume 20 and string coupling 0.5 with supersymmetry broken along Kähler moduli, but only at a hand-tuned parameter point ...
Building an explicit de Sitter
hep-th 2012-08 conditional novelty 6.0 of 10

An explicit type IIB compactification on CP^4_{11169}[18] is constructed in which all geometric moduli are stabilized and the Kähler sector lands in a metastable de Sitter vacuum at volume about 52.
D-Branes at del Pezzo Singularities: Global Embedding and Moduli Stabilisation
hep-th 2012-06 conditional novelty 6.0 of 10

The authors construct compact Calabi-Yau orientifolds with two del Pezzo singularities hosting a trification-like visible sector, and show all Kaehler moduli can be stabilised, giving LARGE Volume de Sitter vacua with...
The type IIB string axiverse and its low-energy phenomenology
hep-th 2012-06 conditional novelty 6.0 of 10

The LARGE Volume Scenario of type IIB string theory generically yields a QCD axion plus many lighter axion-like particles, and explicit brane constructions exist where the QCD axion survives anomalous U(1) mixing with...
Moduli Stabilisation for Chiral Global Models
hep-th 2011-10 conditional novelty 6.0 of 10

An explicit Type IIB Calabi-Yau orientifold with four Kähler moduli is constructed in which all moduli are stabilised inside the Kähler cone while a chiral SU(5)-like brane sector is retained.
Anisotropic Modulus Stabilisation: Strings at LHC Scales with Micron-sized Extra Dimensions
hep-th 2011-05 conditional novelty 6.0 of 10

Poly-instanton corrections in Type IIB flux compactifications stabilise K3-fibred Calabi-Yau geometries with two micron-sized extra dimensions and a TeV string scale.
Testing String Vacua in the Lab: From a Hidden CMB to Dark Forces in Flux Compactifications
hep-th 2011-03 conditional novelty 6.0 of 10

Anisotropic type IIB flux compactifications can produce a GeV-scale hidden photon with mixing near 10^-6 for an intermediate string scale, and with fine-tuning a meV-scale one, opening string vacua to beam-dump and li...

See all 110 Pith citations

How later papers used it

216 later papers cite it

Evidence: substantial. 212 of the citing papers share no author with it, and 16 of those carry a confident label from Pith's citation classifier.

Pith read 20 of the 408 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 compared its own results with it.

Compares with it 1 of 9 papers with this label

Remarked that its finding for the correction to the = 1 Kähler potential is in perfect agreement with the corresponding result in this paper.

The Euler characteristic correction to the Kaehler potential - revisited (2016) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

205 arXiv papers cite this in 398 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 306 sentences without a confident label

Builds on it 1 paper

This form of scalar potential represents an odd moduli generalisation of the results of [ref] .

Systematics of type IIB moduli stabilisation with odd axions · An apparent mismatch in the standard approach · 0.99

Uses its method or tool 4 papers

One uses the warped metric ansatz [equation] together with the term [equation] from the $R^4_10$ correction to the type-IIB action [ref] in 10d Einstein frame.

The LVS Parametric Tadpole Constraint · The LVS Parametric Tadpole Constraint · 0.92
The Becker Becker Haack Louis(BBHL) correction to the Kähler geometry is combined with the Kachru Kallosh Linde Trivedi (KKLT)nonperturbative sector to calculate the volume response, barrier, and Schur correction [ref] .

Penumbral Inflation from Calabi-Yau Boundaries · Introduction · 0.97
Following [ref] we can write the resulting scalar potential in the following form [equation]

A sufficient condition for de Sitter vacua in type IIB string theory · `Kähler uplifting' – a meta-stable dS vacuum for the Kähler modulus · 0.85

Uses its data or values 1 paper

The leading $α'$-corrections were computed in [ref] and the coefficient $ξ_α'$ was found to be of the following form: [equation] where $χ$ is the Euler number of the compactification manifold and $ϕ_0$ is the expectation value of the dilaton (which we assume to be stabilized by fluxes).

Volume modulus inflation and a low scale of SUSY breaking · Corrections to Kähler potential · 0.92

Compares with it 9 papers

We reproduced the result of Becker, Becker, Haack, and Louis (BBHL) [ref] by showing that a correction to the Kähler potential emerges, which is proportional to the Euler characteristic of the leading order Calabi-Yau threefold background.

The Euler characteristic correction to the Kaehler potential - revisited · Conclusions · 0.87
The vacua are obtained due to an interplay of the Euler-Characteristic correction [ref] and the $α'^2$-corrections to the scalar potential.[ The form of the scalar potential due to the $α'^2$-correction obtained in [ref] is similar to the one obtained at order $α'^3$ in [ref] .] We close by emphasizing that the discussion can be performed analogously for Calabi–Yau fourfolds with $χ(B_3) > 0$ which leads to de Sitter extrema.

F-theory Vacua and $\alpha'$-Corrections · Introduction · 0.92
As a non-trivial cross-check of the prescription, we will find the perfect match between the torus amplitude we compute in [ref] with by now a very well-established result in the literature [ref] .

On string one-loop correction to the Einstein-Hilbert term and its implications on the Kahler potential · Introduction · 0.99

Cites it as support 2 papers

Due to the absence of $(α')^1$ corrections in 10D and 8D, and the fact that $(α')^2$ corrections enjoy an extended no-scale cancellation [ref] , we deduced that the dominant no-scale breaking effects at string tree-level arise from known $(α')^3$ corrections [ref] modulo potential logarithmic corrections.

Systematics of the $\alpha'$ Expansion in F-Theory · Conclusions · 0.98
As confirmed by several studies, the leading no-scale breaking effects are $𝒪(α'^3)$ corrections which lift only $𝒱$ [ref] .

Recent progress on inflation and dark energy from string theory · Inflating with string moduli · 0.96

Cites it as background 61 papers

Our starting point is the large volume limit of the low-energy 4D $𝒩=1$ - effective action of type IIB Calabi-Yau-orientifold compactifications with background fluxes [ref] including the leading order $(α')^3$-corrections to the bulk fields [ref] and string-loop corrections [ref] .

Starobinsky-Type Inflation from $\alpha'$-Corrections · The Large Volume Scenario · 0.88
Let us begin with a summary of the inclusion of perturbative $α^'$-corrections to the Kähler potential in type IIB string theory compactified on Calabi-Yau three-folds with NS-NS and RR fluxes turned on, as discussed in [ref] .

Moduli Stabilization, Large-Volume dS Minimum Without anti-D3-Branes, (Non-)Supersymmetric Black Hole Attractors and Two-Parameter Swiss Cheese Calabi-Yau's · Non-supersymmetric dS minimum via Non-perturbative $α^'$- and Instanton Corrections · 0.93
Perturbative LVS: With the inclusion of the so-called log-loop effects [ref] along with the BBHL corrections [ref] , the Kähler potential $K$ is given by Eq. ([ref]) with $Y = V + ξ̂/2 + η̂(lnV -1)$, where $ξ̂= ξ/g_s^3/2$, and $η̂= -g_s^2ξ̂ ζ[2]/ζ[3]$.

Global Embedding of Fibre Inflation in Perturbative LVS · LVS schemes of moduli stabilisation · 0.92

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [17]

K. Becker and M. Becker, “Supersymmetry Breaking, M-Theory and Fluxes”, JHEP 0107:038 (2001), hep-th/0107044

View on Pith Pith review arXiv 2001

[2] [21]

M. Haack and J. Louis, “ M-Theory Compactiﬁed on Calabi-Yau Fourfolds with Back- ground Flux”, Phys. Lett. B507 (2001) 296, hep-th/0103068

View on Pith Pith review arXiv 2001

[3] [32]

S. Ferrara and S. Sabharwal, “Quaternionic Manifolds f or Type II Superstring Vacua of Calabi-Yau Spaces”, Nucl. Phys. B332 (1990) 317

View on Pith 1990

[4] [38]

R. B¨ ohm, H. G¨ unther, C. Herrmann and J. Louis, “Compac tiﬁcation of Type IIB String Theory on Calabi-Yau Threefolds”, Nucl. Phys. B569 (2000) 229, hep- th/9908007

View on Pith 2000

[5] [1]

M. Dine, R. Rohm, N. Seiberg and E. Witten, “Gluino Conden sation in Superstring Models”, Phys. Lett. B156 (1985) 55

View on Pith 1985

[6] [2]

J. P. Derendinger, L. E. Ibanez and H. P. Nilles, “On The Lo w-Energy D = 4, N=1 Supergravity Theory Extracted from the D = 10, N=1 Superstri ng”, Phys. Lett. B155 (1985) 65

View on Pith 1985

[7] [3]

R. Rohm and E. Witten, “The Antisymmetric Tensor Field in Superstring Theory”, Ann. Phys. 170 (1986) 454

View on Pith 1986

[8] [4]

For a recent review see, for example, H. P. Nilles, “Hidde n Sector Supergravity Break- down”, Nucl. Phys. Proc. Suppl. 101 (2001) 237, hep-ph/0106063

View on Pith Pith review arXiv 2001

[9] [5]

S. B. Giddings, S. Kachru and J. Polchinski, “Hierarchie s from Fluxes in String Com- pactiﬁcations”, hep-th/0105097

View on Pith Pith review arXiv

[10] [6]

S. Kachru, M. Schulz and S. Trivedi, “Moduli Stabilizati on from Fluxes in a Simple IIB Orientifold”, hep-th/0201028

View on Pith Pith review arXiv

[11] [7]

A. R. Frey and J. Polchinski, “ N = 3 Warped Compactiﬁcations”, hep-th/0201029

View on Pith Pith review arXiv

[12] [8]

C. Angelantonj and A. Sagnotti, “Open strings”, hep-th/ 0204089

View on Pith

[13] [9]

M. Grana and J. Polchinski, “Supersymmetric Three-Form Flux Perturbations on AdS(5)”, Phys. Rev. D63 (2001) 026001, hep-th/0009211

View on Pith Pith review arXiv 2001

[14] [10]

S.S. Gubser, “Supersymmetry and F -Theory Realization of the Deformed Conifold with Three-Form Flux”, hep-th/0010010

View on Pith Pith review arXiv

[15] [11]

J. Michelson, “Compactiﬁcations of Type IIB Strings to Four Dimensions with Non- Trivial Classical Potential”, Nucl. Phys. B495 (1997) 127, hep-th/9610151

View on Pith Pith review arXiv 1997

[16] [12]

T.R. Taylor and C. Vafa, “R-R Flux on Calabi-Yau and Part ial Supersymmetry Break- ing”, Phys. Lett. B474 (2000) 130, hep-th/9912152

View on Pith Pith review arXiv 2000

[17] [13]

P. Mayr, “On Supersymmetry Breaking in String Theory an d its Realization in Brane Worlds”, Nucl. Phys. B593 (2001) 99, hep-th/0003198

View on Pith Pith review arXiv 2001

[18] [14]

G. Dall’Agata, “Type IIB Supergravity Compactiﬁed on a Calabi-Yau Manifold with H-Fluxes”, JHEP 0111:005 (2001), hep-th/0107264

View on Pith Pith review arXiv 2001

[19] [15]

J. Louis and A. Micu, “Type II Theories Compactiﬁed on Ca labi-Yau Threefolds in the Presence of Background Fluxes”, hep-th/0202168

View on Pith Pith review arXiv

[20] [16]

G. Curio, A. Klemm, D. L¨ ust and S. Theisen, “On the Vacuu m Structure of Type II String Compactiﬁcations on Calabi-Yau Spaces with H-Flu xes”, Nucl. Phys. B609 (2001) 3, hep-th/0012213

View on Pith Pith review arXiv 2001

[21] [18]

K. Becker and M. Becker, “ M-Theory on Eight-Manifolds”, Nucl. Phys. B477 (1996) 155 hep-th/9605053. 24

View on Pith Pith review arXiv 1996

[22] [19]

S. Gukov, C. Vafa and E. Witten, “CFT’s from Calabi-Yau F our-Folds”, Nucl. Phys. B484 (2000) 69, hep-th/9906070

View on Pith Pith review arXiv 2000

[23] [20]

M. Haack and J. Louis, “Duality in Heterotic Vacua with F our Supercharges”, Nucl. Phys. B575 (2000) 107, hep-th/9912181

View on Pith Pith review arXiv 2000

[24] [22]

M. Haack, J. Louis and M. Marquart, “Type IIA and Heterot ic String Vacua in D = 2”, Nucl. Phys. B598 (2001) 30, hep-th/0011075

View on Pith Pith review arXiv 2001

[25] [23]

S. Gukov and M. Haack, “IIA String Theory on Calabi-Yau F ourfolds with Background Fluxes”, hep-th/0203267

View on Pith Pith review arXiv

[26] [24]

C. Beasley and E. Witten, “A Note on Fluxes and Superpote ntials in M-theory Com- pactiﬁcations on Manifolds of G2 Holonomy”, hep-th/0203061

View on Pith Pith review arXiv

[27] [25]

K. Dasgupta, G. Rajesh and S. Sethi, “ M-Theory, Orientifolds and G-Flux”, JHEP 9908:023 (1999), hep-th/9908088

View on Pith Pith review arXiv 1999

[28] [26]

E. J. Cremmer, B. Julia and L. Scherk, “Supergravity The ory in Eleven Dimensions”, Phys. Lett. B5 (1978) 409

View on Pith 1978

[29] [27]

A. Kehagias and H. Partouche, “The Exact Quartic Eﬀecti ve Action for the Type IIB Superstring”, Phys. Lett. B422 (1998) 109, hep-th/9710023

View on Pith Pith review arXiv 1998

[30] [28]

K. Peeters, P. Vanhove and A. Westerberg, “Supersymmet ric Higher Derivative Actions in Ten Dimensions and Eleven Dimensions, the Associ ated Superalgebras and their Formulation in Superspace”, Class. Quantum Grav. 18 (2001) 843, hep- th/0010167

View on Pith 2001

[31] [29]

S. Frolov, I. Klebanov and A. Tseytlin, “String Correct ions to the Holographic RG Flow of Supersymmetric SU (N ) ×SU (N +M ) Gauge Theory”, Nucl. Phys. B620 (2002) 84, hep-th/0108106

View on Pith Pith review arXiv 2002

[32] [30]

K. Peeters, P. Vanhove and A. Westerberg, “Chiral Split ting and World Sheet Grav- itinos in Higher Derivative String Amplitudes”, hep-th/01 12157

View on Pith

[33] [31]

M.B. Green, “Interconnections Between Type II Superst rings, M-theory and N = 4 Supersymmetric Yang-Mills”, hep-th/9903124

View on Pith Pith review arXiv

[34] [33]

I. Antoniadis, S. Ferrara, R. Minasian and K. S. Narain, “R4 Couplings in M and Type II Theories on Calabi-Yau Spaces”, Nucl. Phys. B507 (1997) 571, hep-th/9707013

View on Pith Pith review arXiv 1997

[35] [34]

D. Gross and E. Witten, “Superstring Modiﬁcation of Ein stein Equations”, Nucl. Phys. B277 (1986) 1

View on Pith 1986

[36] [35]

M.D. Freeman and C.N. Pope, “Beta-Functions and Supers tring Compactiﬁcations”, Phys. Lett. B174 (1986) 48. 25

View on Pith 1986

[37] [36]

M. T. Grisaru, A. E. M. van de Ven and D. Zanon, “Four-Loop Divergences for the N = 1 Supersymmetric Non-Linear Sigma-Model in Two Dimension s”, Nucl. Phys. B277 (1986) 409

View on Pith 1986

[38] [37]

P. Candelas, X. C. De La Ossa, P. S. Green and L. Parkes, “A Pair of Calabi-Yau Manifolds as an Exactly Soluble Superconformal Field Theor y”, Nucl. Phys. B359 (1991) 21

View on Pith 1991

[39] [39]

M. Bodner and A. C. Cadavid, “Dimensional Reduction of t he Type IIB Supergravity and Exceptional Quaternionic Manifolds”, Class. Quantum Grav. 7 (1990) 829

View on Pith 1990

[40] [40]

C.W. Misner, K.S. Thorne and J.A. Wheeler, “Gravitatio n”, Freeman, San Francisco (1973)

View on Pith 1973

[41] [41]

M.T. Grisaru, A.E. van de Ven and D. Zanon, “Four Loop Bet a Function for fhe N = 1 and N = 2 Supersymmetric Nonlinear Sigma Model in Two Dimensions” , Phys. Lett. B173 (1986) 423

View on Pith 1986

[42] [42]

M. T. Grisaru, A.E.M. van de Ven and D. Zanon, “Two-dimen sional Supersymmetric Sigma Models on Ricci Flat K¨ ahler Manifolds are not Finite” , Nucl. Phys. B277 (1986) 388

View on Pith 1986

[43] [43]

L. Andrianopoli, R. D’Auria and S. Ferrara, “Supersymm etry Reduction of N - Extended Supergravities in Four Dimensions”, JHEP 0203:025 (2002), hep-th/0110277

View on Pith Pith review arXiv 2002

[44] [44]

L. Andrianopoli, R. D’Auria and S. Ferrara, “Consisten t Reduction of N = 2 → N = 1 Four Dimensional Supergravity Coupled to Matter”, Nucl. Phys. B628 (2002) 387, hep-th/0112192

View on Pith Pith review arXiv 2002

[45] [45]

A. Sen, “Central Charge of the Virasoro Algebra for Supe rsymmetric Sigma Models on Calabi-Yau Manifolds”, Phys. Lett. B178 (1986) 370

View on Pith 1986

[46] [46]

M.D. Freeman, C.N. Pope, M.F. Sohnius and K.S. Stelle, “ Higher Order σ-Model Counterterms and the Eﬀective Action for Superstrings”, Phys. Lett. B178 (1986) 199

View on Pith 1986

[47] [47]

P. Candelas, M.D. Freeman, C.N. Pope, M.F. Sohnius and K .S. Stelle, “Higher Order Corrections to Supersymmetry and Compactiﬁcations of the H eterotic String”, Phys. Lett. B177 (1986) 341

View on Pith 1986

[48] [48]

J. Polchinski, “String Theory”, 2 vols., Cambridge University Press (1998)

View on Pith 1998

[49] [49]

E. Witten, “New Issues in Manifolds of SU (3) Holonomy”, Nucl. Phys. B268 (1986) 79

View on Pith 1986

[50] [50]

P.S. Howe and P.C. West, “The Complete N = 2, D = 10 Supergravity”, Nucl. Phys. B238 (1984) 181

View on Pith 1984

[51] [51]

A. A. Tseytlin, “ R4 Terms in 11 Dimensions and Conformal Anomaly of (2 , 0) The- ory”, Nucl. Phys. B584 (2000) 233, hep-th/0005072. 26

View on Pith Pith review arXiv 2000

[52] [52]

E. J. Cremmer and S. Ferrara, “Formulation of Eleven-Di mensional Supergravity in Superspace”, Phys. Lett. B91 (1980) 61; L. Brink and P. Howe, “Eleven-Dimensional Supergravity on the Mass-Shell in Superspace”, Phys. Lett. B91 (1980) 384

View on Pith 1980

[53] [53]

A. Strominger, “Loop Corrections to the Universal Hype rmultiplet”, Phys. Lett. B421 (1998) 139, hep-th/9706195

View on Pith Pith review arXiv 1998

[54] [54]

T. Banks, “Cosmological Breaking of Supersymmetry? or Little Lambda Goes Back to the Future 2”, hep-th/0007146

View on Pith Pith review arXiv

[55] [55]

M. T. Grisaru and D. Zanon, “Sigma-Model Superstring Co rrections to the Einstein Hilbert Action”, Phys. Lett. B177 (1986) 347

View on Pith 1986

[56] [56]

Q.H. Park and D. Zanon, “More on Sigma Model Beta Functio ns and Low-Energy Eﬀective Actions”, Phys. Rev. D35 (1987) 4038. 27

View on Pith 1987