Moduli Stabilization in Type IIB Orientifolds (II)

D. Lust; E. Scheidegger; S. Reffert; S. Stieberger; W. Schulgin

REVIEW

Moduli Stabilization in Type IIB Orientifolds (II)

D. Lust, S. Reffert, E. Scheidegger, W. Schulgin, S. Stieberger

High Energy Physics - Theory · Submitted 4 Sep 2006 · 57 references

Pith's verdict: A clean, general no-go diagnostic for KKLT without complex structure moduli, plus two explicit all-moduli-fixed resolved orbifolds — with one exclusion argument asserted rather than shown.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-th/0609013 (version 2)

Pith IDBZITS7VN, Pith's permanent record of this paper and its review

CitationD. Lust, E. Scheidegger, S. Reffert, S. Stieberger, W. Schulgin. "Moduli Stabilization in Type IIB Orientifolds (II)." arXiv:hep-th/0609013 (2006). https://pith.science/paper/BZITS7VN

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The thing to take away: criteria (2.36)/(2.40) are a genuinely useful, cheap diagnostic. They depend only on the Kähler potential K(T+T̄), not on flux parameters or racetrack coefficients, and the translation to (2.45)/(2.46) via the special-geometry relations (2.43)/(2.44) is clean. The paper is also honest about sufficiency: the Z4 and X8 examples show cases where (2.45) fails but instability persists, and it says so. That kind of self-check is rarer than it should be, and it earns the paper credit. The second contribution, §3's mechanism for H^{1,1}_- — impose B∧J=0 on the odd cycles, get K_{ãa}b^ã=0, note the same condition falls out of the D-term for a D7 stack, and let the axions c^a be eaten by a U(1) — is a proposal rather than a proof, but a sensible one that plugs a real hole in the KKLT story for these geometries. §5.4 is the meat: 19 Kähler moduli fixed for resolved Z6-II, 61 for Z2×Z4, with explicit flux integers and divisor volumes. Real work, though it leans on [4] for intersection numbers and divisor topologies, and the flux scan is not shipped as code. Where it is soft: §5.5. The general argument — N has block form (5.53) with positive entries, so the new Kähler coordinates come out positive — is plausible, but it is worked out only for Z2×Z2, which is not in the excluded list (h_{2,1}=3). For Z4×Z4, Z6×Z6, Z2×Z6' and Z8-I the paper says only 'similarly may be verified.' The X8 example in §2.3 shows a legitimate divisor basis can give t_1<0, so this needs checking case by case, and the checks are not displayed. Second, for Z3, Z7 and Z3×Z3, Table 4 gives h^{(-)}_{1,1}=13, 9, 37 ≠ 0, while (2.45) was derived under h^{(-)}_{1,1}=0. The conclusion survives via §3's independent mass argument, but the stated route is not justified as written. On the reader's weakest-assumption pick: α' corrections are acknowledged in the concluding remarks, so that is not the sharp edge. The §5.5 gap is. Who it is for: people building KKLT models on orbifolds who want a quick filter before doing the hard work. Worth a serious referee.

Referee report

Significance

The no-go criteria are a compact, model-independent diagnostic that can be applied directly to a Kähler potential without solving the full F-term equations, and the explicit stabilizations are a concrete demonstration that the KKLT racetrack can be realized on resolved toroidal orientifolds with large volume. The paper is a solid contribution to the flux-compactification literature. Strengths worth naming: the derivation of the determinant formula (2.35) and the minor formula (2.39) is clean and the criteria are correctly stated as sufficient, not necessary, conditions for instability; the zero-mode counting in Section 4 and Tables 2 and 5 is a useful compilation; and the explicit flux integers and divisor volumes in Section 5.4 make the stabilization reproducible in principle.

Major objections (3)

[§5.5, Eqs. (5.52)-(5.54)] The resolved-geometry half of the headline claim is asserted rather than shown for four of the seven listed orbifolds. The only worked example is Z2xZ2 (Eqs. 5.55-5.65), and Z2xZ2 has h_{2,1}=3 (Table 3), so it is not itself in the excluded list. For Z4xZ4, Z6xZ6, Z2xZ6' and Z8-I the paper states only that 'similarly, the condition (2.45) may be verified.' The general argument rests on the block form (5.53) with λ, μ, ρ ∈ Q_+ and on the heuristic that the blow-up moduli are 'generically very small.' The X8 example (Eqs. 2.60, 2.64) shows that a legitimate divisor basis can give t_1 < 0, in which case (2.45) does not apply and one must fall back to (2.46). A concrete test: display N and the resulting t_i for at least one of Z4xZ4, Z6xZ6, Z2xZ6', Z8-I, or replace the heuristic with a proof that the block form (5.53) with positive entries holds for each case from the toric data of [4].
[§2.2 vs §5.5, Table 4] Criterion (2.45) is derived in §2.3 under the assumption h^{(-)}_{1,1}(X6)=0, stated explicitly at the top of §2.2. But §5.5 applies (2.45) to Z3, Z7 and Z3xZ3, for which Table 4 gives h^{(-)}_{1,1}=13, 9 and 37 respectively. When h^{(-)}_{1,1}≠0 the Kähler potential depends on the G^a through (2.10)/(2.11), and the special-geometry relation (2.44) is not obviously preserved. Section 3 does supply an independent argument for those cases (negative masses for g^a_1, Eq. 3.5, and zero masses for g^a_2, Eq. 3.6), so the conclusion may survive, but §5.5 does not invoke it. A concrete test: state whether (2.45) is claimed to hold when h^{(-)}_{1,1}≠0, and if so re-derive (2.44) in the presence of the G^a-dependent K_KM; otherwise route the Z3, Z7, Z3xZ3 exclusions through §3 explicitly.
[§5.4(i) and abstract] The claim that 'all 27 moduli' are stabilized for Z6-II includes the six c^a, which are fixed by the mechanism proposed in §3 (ambient 2-form flux Yf_2 plus U(1) Stückelberg), not by explicit flux integers. Only the b^a are fixed explicitly, via det(K)=-91.25≠0 giving b^a=0. The abstract's 'we fix all moduli through a combination of fluxes and racetrack superpotential' therefore overstates what is demonstrated for Z6-II; for Z2xZ4 (h^{(-)}_{1,1}=0) the claim is fully demonstrated. A concrete test: give the Yf_2 flux integers for the Z6-II model and verify that the gauging (3.18) is realized, or qualify the abstract and §5.4(i) to say that the c^a are fixed by the proposed mechanism of §3.

Minor objections (8)

[Abstract] The abstract lists six excluded orbifolds (Z3, Z7, Z3xZ3, Z4xZ4, Z6xZ6, Z2xZ6') while §5.5 and the concluding remarks add Z8-I on SU(4)^2; the two lists should agree. The abstract also writes h_{2,1}(X6)=0 whereas the criterion is on h^{(-)}_{2,1}(X6); the distinction matters for orientifolds such as Z6-II on SU(2)xSU(6), where h_{2,1}(Y6)=1.
[§2.3, after Eq. (2.46)] The sentence 'If all of them are positive, i.e. t_j > 0, the mass matrix M for the axions is negative definite' overstates the result: det(M)<0 implies M is not positive definite, not that it is negative definite. The weaker statement is the one used.
[§2.3, paragraph after Eq. (2.46)] The displayed relation 'K_i t_i = 4/3 Vol(D_i) t_i = K = 6 Vol(X6) > 0' appears to be missing a sum over i; as written it would imply each t_i K_i = K, which is too strong. The correct relation is Σ_i t^i K_i = 3K, which still yields at least one positive t_k when all Vol(D_i)>0.
[§5.4(i), after Eq. (5.38)] Several divisor volumes in (5.38) are of order 0.7-1.0 (E4, E1,γ, E3,γ), so the phrase 'large enough to suppress higher order instanton effects' is a stretch in words even if the numerical expansion parameter e^{-2π·0.71}≈0.012 is small. Stating the expansion parameter explicitly would be clearer.
[§2.3, Eq. (2.35)] The determinant formula (2.35) and the minor formula (2.39) are quoted 'after some tedious algebra.' Given that these are the load-bearing technical results of the no-go, an appendix with the intermediate steps, or at least a statement of which identities from §2.1 are used, would help the reader verify them.
[§4, Table 2] The 'number of zero modes' row of Table 2 is hard to parse: the bracketed terms and the signs of the h^{(0,1)}, h^{(0,2)} contributions are not explained in the caption. A short legend would make the table usable.
[§5.2] The paper states that requirements (i) and (ii) are met by T^6/Z4 on SU(4)^2, T^6/Z6-II on SU(2)xSU(6), T^6/Z2xZ2 and T^6/Z2xZ4, and that 'we expect that all geometric moduli can be stabilized in these cases,' but §5.4 works out only Z6-II and Z2xZ4. The status of Z4 on SU(4)^2 and Z2xZ2 should be stated explicitly as not checked in this paper.
[Abstract] Typographical: 'stablization', 'accociated', and 'Kaehler' in the abstract should read 'stabilization', 'associated', and 'Kähler'.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

A criterion on the Kähler potential decides in advance whether a KKLT compactification can survive its uplift to positive vacuum energy — and it eliminates seven families of toroidal orbifolds.

The reading

The paper asks a narrow but consequential question: when a type IIB string compactification is put through the KKLT recipe — fluxes to freeze the shape moduli and the dilaton, non-perturbative effects to freeze the sizes of internal cycles, then an anti-brane to lift the negative AdS energy to a tiny positive one — does the resulting AdS minimum actually survive the lift? The authors derive a criterion that depends only on the Kähler potential of the size moduli and not on any flux parameter, and show that when it holds, the mass matrix of the axionic partners has a negative eigenvalue, so the uplifted vacuum is unstable. Applied to compactifications with no complex-structure moduli, the criterion eliminates a whole family of toroidal orbifolds at a stroke, at the orbifold point and after the singularities are blown up. The paper then does the constructive half: a mechanism for the moduli that live in the odd cohomology, and two fully worked resolved orbifolds in which every modulus is fixed by fluxes plus a racetrack superpotential.

What carries the argument

The load-bearing object is the axion mass matrix $M$ of equation (2.33), built from second derivatives of the $F$-term potential at the supersymmetric point, together with its determinant expressed in terms of principal minors (equation 2.35) and the one-minor formula (equation 2.39). Its negativity is decided not by dynamics but by the sign of first Kähler derivatives, which the Legendre-transform identities $K_{T^i}=-2t^i/K$ and $K_{T^iT^j}=G_{ij}/K^2$ convert into statements about the Kähler cone and the diagonal intersection numbers $K_{ii}$. Two secondary mechanisms carry the rest of the paper: the divisor index $chi_{D3}=tfrac12(N_+-N_-)$, computed case by case for the four divisor topologies $K3$, $T^4$, $P^1times T^2$ and rational surfaces, which decides whether a Euclidean D3-brane or a gaugino condensate can generate a non-perturbative term at all; and the calibration condition $B_2wedge J=0$ on a wrapped four-cycle, which supplies the linear system that pins the odd-cohomology moduli.

Extended reading notes

Core claim

For a type IIB orientifold with $h^{(-)}_{2,1}(X_6)=0$ and $n$ Kähler moduli, the authors evaluate the scalar potential at a supersymmetric AdS minimum and compute the mass matrix $M$ of the axions. They show that $M$ fails to be positive definite — so no controlled uplift to de Sitter is possible — whenever all first derivatives satisfy $K_{T^i}<0$, and also whenever some $K_{T^i}<0$ together with $(-1)^n$ times the principal minor $O_i$ of $O_{ij}=-K_{T^iT^j}+tfrac12 K_{T^i}K_{T^j}$ is non-positive. Using $K_{T^i}=-2t^i/K$ and the signature $(1,n-1)$ of the intersection form, these become the clean statements $t^i>0$ and $K_{ii}geq 0$ in Kähler-cone coordinates. Because at least one $t^k$ is always positive, the second criterion collapses to reading off a single diagonal intersection number. This rules out a stable KKLT uplift for $Z_3$, $Z_7$, $Z_3times Z_3$, $Z_4times Z_4$, $Z_6times Z_6$, $Z_2times Z_6'$ and $Z_8$-I on the $SU(4)^2$ lattice, both at the orbifold point and after resolution, since the resolved Kähler coordinates turn out to be positive linear combinations of the original ones. On the constructive side the authors propose fixing the $H^{(1,1)}_-$ moduli through the calibration condition $B_2wedge J=0$, which forces $K_{aa b}b^a=0$ and hence $b^a=0$, while the axions $c^a$ are eaten by a $U(1)$ made massive through the Stückelberg coupling; and they exhibit the resolved $Z_{6-II}$ orbifold on $SU(2)times SU(6)$ with all 27 moduli fixed and the resolved $Z_2times Z_4$ orbifold on $SU(2)^2times SO(5)^2$ with all 63 moduli fixed.

Load-bearing premise

The instability criteria are derived for a Kähler potential of the tree-level form $K(T+bar T)$ together with a racetrack superpotential, so they say nothing about vacua whose stabilization depends on $alpha'$ or string-coupling corrections that break that structure — a limitation the authors themselves flag in their concluding remarks.

Editorial extensions

If this is right

Seven families of toroidal orbifold orientifolds with $h^{(-)}_{2,1}(X_6)=0$ are removed from the list of viable KKLT backgrounds, so effort on them can be redirected rather than spent searching for minima that cannot be stable after uplift.
The obstruction is a property of the Kähler potential alone: it can be checked before any flux tuning, by inspecting the signs of $t^i$ and the diagonal intersection numbers $K_{ii}$ of the candidate manifold.
The odd-cohomology moduli $b^a$ and $c^a$, previously a loose end in orientifold model building, acquire a stabilization mechanism that does not disturb the Kähler moduli already fixed by instantons.
The resolved $Z_{6-II}$ and $Z_2times Z_4$ orientifolds become explicit, fully stabilized vacua with small string coupling and large volume, usable as concrete backgrounds for further study.
Manifolds whose fixed lines fall into orbits longer than one tend to give $P^1times T^2$ divisors that never contribute, so complete stabilization by instantons alone is expected to be non-generic.

Reading between the lines

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

The criterion is a statement about the sign pattern of the Kähler potential, so it should extend to any compactification whose moduli space has the same special-geometry structure, not only to toroidal orbifolds; testing it on a non-toroidal Calabi-Yau with $h^{(-)}_{2,1}=0$ would be a clean check of scope.
Because the obstruction lives at the level of the axion mass matrix, $\alpha'$ and $g_s$ corrections that preserve the $K(T+\bar T)$ form cannot rescue these models; only corrections that break that structure can, which makes the size of such corrections the natural next calculation.
The two worked examples fix dozens of moduli with a racetrack whose exponentials are of order $10^{-2}$ or smaller, so the neglected multi-instanton terms are a computable, not merely assumed, correction — a good target for a follow-up.
The zero-mode tables suggest a selection principle for model building: choose orientifold actions whose O7-planes intersect every contributing divisor in at least one complex dimension, which is a discrete, enumerable criterion over the orbifold list.

Original abstract

We discuss general properties of moduli stablization in KKLT scenarios in type IIB orientifold compactifications. In particular, we find conditions for the Kaehler potential to allow a KKLT scenario for a manifold X_6 without complex structure moduli, i.e. h_(2,1)(X_6)=0. This way, a whole class of type IIB orientifolds with h_(2,1)(X_6)=0 is ruled out. This excludes in particular all Z_N- and Z_N x Z_M-orientifolds X_6 with h_(2,1)(X_6)=0 for a KKLT scenario. This concerns Z_3, Z_7, Z_3 x Z_3, Z_4 x Z_4, Z_6 x Z_6 and Z_2 x Z_6' -both at the orbifold point and away from it. Furthermore, we propose a mechanism to stabilize the Kaehler moduli accociated to the odd cohomology H^(1,1)_-(X_6). In the second part of this work we discuss the moduli stabilization of resolved type IIB Z_N- or Z_N x Z_M - orbifold/orientifold compactifications. As examples for the resolved Z_6 and Z_2 x Z_4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,458 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.16 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We discuss general properties of moduli stablization in KKLT scenarios in type IIB orientifold compactifications. In particular, we find conditions for the Kaehler potential to allow a KKLT scenario for a manifold X_6 without complex structure moduli, i.e. h_(2,1)(X_6)=0. This way, a whole class of type IIB orientifolds with h_(2,1)(X_6)=0 is ruled out. This excludes in particular all Z_N- and Z_N x Z_M-orientifolds X_6 with h_(2,1)(X_6)=0 for a KKLT scenario. This concerns Z_3, Z_7, Z_3 x Z_3, Z_4 x Z_4, Z_6 x Z_6 and Z_2 x Z_6' -both at the orbifold point and away from it. Furthermore, we propose a mechanism to stabilize the Kaehler moduli accociated to the odd cohomology H^(1,1)_-(X_6). In the second part of this work we discuss the moduli stabilization of resolved type IIB Z_N- or Z_N x Z_M - orbifold/orientifold compactifications. As examples for the resolved Z_6 and Z_2 x Z_4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.

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 discuss general properties of moduli stablization in KKLT scenarios in type IIB orientifold compactifications.	contribution 0.68	0.72	0.05	asserted 0.64
s1	In particular, we find conditions for the Kaehler potential to allow a KKLT scenario for a manifold X_6 without complex structure moduli, i.e. h_(2,1)(X_6)=0.	result 0.89	0.94	0.22	asserted 1.00
s2	This way, a whole class of type IIB orientifolds with h_(2,1)(X_6)=0 is ruled out.	interpretation 0.55	0.83	0.27	asserted 1.00
s3	This excludes in particular all Z_N- and Z_N x Z_M-orientifolds X_6 with h_(2,1)(X_6)=0 for a KKLT scenario.	result 0.71	0.84	0.24	asserted 1.00
s4	This concerns Z_3, Z_7, Z_3 x Z_3, Z_4 x Z_4, Z_6 x Z_6 and Z_2 x Z_6' -both at the orbifold point and away from it.	result 0.85	0.73	0.10	asserted 0.98
s5	Furthermore, we propose a mechanism to stabilize the Kaehler moduli accociated to the odd cohomology H^(1,1)_-(X_6).	contribution 0.97	0.87	0.12	asserted 0.59
s6	In the second part of this work we discuss the moduli stabilization of resolved type IIB Z_N- or Z_N x Z_M - orbifold/orientifold compactifications.	contribution 0.90	0.85	0.07	asserted 0.92
s7	As examples for the resolved Z_6 and Z_2 x Z_4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.	contribution 0.50	0.93	0.14	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Schematic picture of the fixed set configuration of Z6−II on SU(2) × SU(6) The configuration of the fixed point set is displayed in

**Figure 2.** Toric diagram of the resolution of C3/Z6−II and dual graph is a blow–up of F1 in two points, while the remaining exceptional divisors E2,β, E3,γ, E4,β are all P1 ×P1 . D1, D2β, D3γ are blow–ups of P1 ×P1 in 12, 8, and 9 points, respectively. Finally, R1 is a T 4 and R2, R3 are K3 surfaces. Any orientifold projection O with O3– and O7–planes is such that the twelve divisors E1,2γ, E1,3γ, E2,2, E2,3, E4,2, and E4,3 are not invariant under the orientifold action σ [4]: σ E1,2γ = E1,3γ , σ E1,3γ = E1,2γ , σ E2,2 = E2,3 , σ E2,3 = E2,2 , σ E4,2 = E4,3 , σ E4,3 = E4,2 , (5.27) and the six…

**Figure 3.** Schematic picture of the fixed set configuration of Z2 × Z4

**Figure 4.** Toric diagram of two of the resolutions of C3/Z2 × Z4 and dual graphs The resolution is described by the toric diagram in

**Figure 5.** Toric diagram of the resolution of C3/Z2 × Z2 and its dual graph The topology of these divisors was determined in [4]. The divisors E1,αγ and E6,αβ are blow–ups of P1 × P1 in 5 points, the divisors E1,α3, E3,µ, µ = 3, 6, . . ., 10, E6,α3, and D1α are blow–ups of P1 × P1 in 4 points, the divisors E3,µ, µ = 1, 2, 4, 5 are blow–ups of P1 × P1 in 8 points. The divisors E2,βγ, E4,βγ, D2β′ , and D3γ′ are P1 × P1 , while the divisors E5,αβγ are F1, and the Ri are K3 surfaces. The orientifold projection O leaves all the divisors (5.41) and (5.42) invariant, hence h (−) (1,1)(X6) = 0 (cf.…

Figures reproduced from arXiv:hep-th/0609013 by the authors.

References

Works cited (57)

[4]

D. L¨ ust, S. Reﬀert, E. Scheidegger, S. Stieberger “Reso lved Toroidal Orbifolds and their Orientifolds,” arXiv:hep-th/0609014

View on Pith Pith review arXiv
[1]

S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, “De Sitt er vacua in string theory,” Phys. Rev. D 68, 046005 (2003) [arXiv:hep-th/0301240]

View on Pith Pith review arXiv 2003
[2]

C.P. Burgess, R. Kallosh and F. Quevedo, “de Sitter strin g vacua from supersymmetric D-terms,” JHEP 0310, 056 (2003) [arXiv:hep-th/0309187]

View on Pith Pith review arXiv 2003
[3]

D. L¨ ust, S. Reﬀert, W. Schulgin and S. Stieberger, “Modu li stabilization in type IIB orientifolds. I,” arXiv:hep-th/0506090

View on Pith Pith review arXiv
[5]

S. Reﬀert and E. Scheidegger, “Moduli stabilization in t oroidal type IIB orientifolds,” Fortsch. Phys. 54, 462 (2006) [arXiv:hep-th/0512227]

View on Pith Pith review arXiv 2006
[6]

F. Gmeiner, R. Blumenhagen, G. Honecker, D. L¨ ust and T. W eigand, “One in a billion: MSSM-like D-brane statistics,” JHEP 0601, 004 (2006) [arXiv:hep-th/0510170]

View on Pith Pith review arXiv 2006
[7]

S. B. Giddings, S. Kachru and J. Polchinski, “Hierarchie s from ﬂuxes in string com- pactiﬁcations,” Phys. Rev. D 66, 106006 (2002) [arXiv:hep-th/0105097]

View on Pith Pith review arXiv 2002
[8]

S. Gukov, C. Vafa and E. Witten, “CFT’s from Calabi-Yau fo ur-folds,” Nucl. Phys. B 584, 69 (2000) [Erratum-ibid. B 608, 477 (2001)] [arXiv:hep-th/9906070]; T.R. Taylor and C. Vafa, “RR ﬂux on Calabi-Yau and partial sup ersymmetry break- ing,” Phys. Lett. B 474, 130 (2000) [arXiv:hep-th/9912152]; P. Mayr, “On supersymmetry breaking in string theory and it...

View on Pith Pith review arXiv 2000
[9]

E. Witten, “Non-Perturbative Superpotentials In Strin g Theory,” Nucl. Phys. B 474, 343 (1996) [arXiv:hep-th/9604030]

View on Pith Pith review arXiv 1996
[10]

S. Ferrara, L. Girardello and H.P. Nilles, “Breakdown O f Local Supersymmetry Through Gauge Fermion Condensates,” Phys. Lett. B 125, 457 (1983); M. Dine, R. Rohm, N. Seiberg and E. Witten, “Gluino Condensat ion In Superstring Models,” Phys. Lett. B 156, 55 (1985)

View on Pith 1983
[11]

P. Breitenlohner and D.Z. Freedman, “Stability In Gaug ed Extended Supergravity,” Annals Phys. 144, 249 (1982)

View on Pith 1982
[12]

B. Acharya, M. Aganagic, K. Hori and C. Vafa, “Orientifo lds, mirror symmetry and superpotentials,” arXiv:hep-th/0202208

View on Pith Pith review arXiv
[13]

I. Brunner and K. Hori, “Orientifolds and mirror symmet ry,” JHEP 0411, 005 (2004) [arXiv:hep-th/0303135]

View on Pith Pith review arXiv 2004
[14]

T.W. Grimm and J. Louis, “The eﬀective action of N = 1 Cala bi-Yau orientifolds,” Nucl. Phys. B 699, 387 (2004) [arXiv:hep-th/0403067]; T.W. Grimm, “The eﬀective action of type II Calabi-Yau orien tifolds,” Fortsch. Phys. 53, 1179 (2005) [arXiv:hep-th/0507153] 66

View on Pith Pith review arXiv 2004
[15]

F. Denef, M.R. Douglas and B. Florea, “Building a better racetrack,” JHEP 0406, 034 (2004) [arXiv:hep-th/0404257]

View on Pith Pith review arXiv 2004
[16]

F. Denef, M.R. Douglas, B. Florea, A. Grassi and S. Kachr u, “Fixing All Moduli in a Simple F-Theory Compactiﬁcation,” arXiv:hep-th/0503124

View on Pith Pith review arXiv
[17]

L. G¨ orlich, S. Kachru, P.K. Tripathy and S.P. Trivedi, “Gaugino condensation and nonperturbative superpotentials in ﬂux compactiﬁcations ,” JHEP 0412, 074 (2004) [arXiv:hep-th/0407130]

View on Pith Pith review arXiv 2004
[18]

D. L¨ ust, P. Mayr, S. Reﬀert and S. Stieberger, “F-theor y ﬂux, destabilization of ori- entifolds and soft terms on D7-branes,” Nucl. Phys. B 732, 243 (2006) [arXiv:hep- th/0501139]

View on Pith 2006
[19]

D. L¨ ust, S. Reﬀert and S. Stieberger, “MSSM with soft SU SY breaking terms from D7-branes with ﬂuxes,” Nucl. Phys. B 727, 264 (2005) [arXiv:hep-th/0410074]

View on Pith Pith review arXiv 2005
[20]

K. Choi, A. Falkowski, H.P. Nilles and M. Olechowski, “S oft supersymmetry break- ing in KKLT ﬂux compactiﬁcation,” Nucl. Phys. B 718, 113 (2005) [arXiv:hep- th/0503216]

View on Pith 2005
[21]

M.J. Duﬀ, B.E.W. Nilsson and C.N. Pope, “Kaluza-Klein S upergravity,” Phys. Rept. 130, 1 (1986)

View on Pith 1986
[22]

B. de Carlos, S. Gurrieri, A. Lukas and A. Micu, “Moduli s tabilisation in heterotic string compactiﬁcations,” JHEP 0603, 005 (2006) [arXiv:hep-th/0507173]

View on Pith Pith review arXiv 2006
[23]

D. L¨ ust and S. Stieberger, “Gauge threshold correctio ns in intersecting brane world models,” arXiv:hep-th/0302221

View on Pith Pith review arXiv
[24]

K. Choi, A. Falkowski, H.P. Nilles, M. Olechowski and S. Pokorski, “Stability of ﬂux compactiﬁcations and the pattern of supersymmetry brea king,” JHEP 0411, 076 (2004) [arXiv:hep-th/0411066]

View on Pith Pith review arXiv 2004
[25]

S. P. de Alwis, “Eﬀective potentials for light moduli,” Phys. Lett. B 626, 223 (2005) [arXiv:hep-th/0506266]

View on Pith Pith review arXiv 2005
[26]

H. Abe, T. Higaki and T. Kobayashi, “Remark on integrati ng out heavy moduli in ﬂux compactiﬁcation,” Phys. Rev. D 74, 045012 (2006) [arXiv:hep-th/0606095]; H.X. Yang, “On moduli stabilization scheme in type IIB ﬂux co mpactiﬁcations,” arXiv:hep-th/0608155; “Moduli stabilization in type IIB ﬂ ux compactiﬁcations,” Phys. Rev. D 73, 066006 (2006) [arXiv:hep...

View on Pith Pith review arXiv 2006
[27]

R.A. Horn and C.R. Johnson “Matrix Analysis”, Cambridg e University Press, 1990

View on Pith 1990
[28]

R. D’Auria, S. Ferrara and M. Trigiante, “c-map,very sp ecial quaternionic geometry and dual K¨ ahler spaces,” Phys. Lett. B 587, 138 (2004) [arXiv:hep-th/0401161]

View on Pith Pith review arXiv 2004
[29]

P. Candelas and X. de la Ossa, “Moduli Space Of Calabi-Ya u Manifolds,” Nucl. Phys. B 355, 455 (1991)

View on Pith 1991
[30]

J.J. Blanco-Pillado, C.P. Burgess, J.M. Cline, C. Esco da, M. Gomez-Reino, R. Kallosh, A. Linde and F. Quevedo, “Inﬂating in a better racetrack,” ar Xiv:hep-th/0603129

View on Pith Pith review arXiv
[31]

J.P. Conlon, “The QCD axion and moduli stabilisation,” arXiv:hep-th/0602233. 67

View on Pith Pith review arXiv
[32]

M. Marino, R. Minasian, G.W. Moore and A. Strominger, “N onlinear instantons from supersymmetric p-branes,” JHEP 0001, 005 (2000) [arXiv:hep-th/9911206]

View on Pith Pith review arXiv 2000
[33]

H. Jockers and J. Louis, “The eﬀective action of D7-bran es in N = 1 Calabi-Yau orientifolds,” Nucl. Phys. B 705, 167 (2005) [arXiv:hep-th/0409098]; “D-terms and F- terms from D7-brane ﬂuxes,” Nucl. Phys. B 718, 203 (2005) [arXiv:hep-th/0502059]; H. Jockers, “The eﬀective action of D-branes in Calabi-Yau o rientifold compactiﬁca- tions,” Fortsch. Phys. 53...

View on Pith Pith review arXiv 2005
[34]

M. Dine, N. Seiberg and E. Witten, “Fayet-Iliopoulos Te rms In String Theory,” Nucl. Phys. B 289, 589 (1987)

View on Pith 1987
[35]

L.E. Ibanez, F. Marchesano and R. Rabadan, “Getting jus t the standard model at intersecting branes,” JHEP 0111, 002 (2001) [arXiv:hep-th/0105155]

View on Pith Pith review arXiv 2001
[36]

I. Antoniadis and T. Maillard, “Moduli stabilization f rom magnetic ﬂuxes in type I string theory,” Nucl. Phys. B 716, 3 (2005) [arXiv:hep-th/0412008]

View on Pith Pith review arXiv 2005
[37]

A.K. Kashani-Poor and A. Tomasiello, “A stringy test of ﬂux-induced isometry gaug- ing,” Nucl. Phys. B 728, 135 (2005) [arXiv:hep-th/0505208]

View on Pith Pith review arXiv 2005
[38]

R. Kallosh and D. Sorokin, “Dirac action on M5 and M2 bran es with bulk ﬂuxes,” JHEP 0505, 005 (2005) [arXiv:hep-th/0501081]

View on Pith Pith review arXiv 2005
[39]

N. Saulina, “Topological constraints on stabilized ﬂu x vacua,” Nucl. Phys. B 720, 203 (2005) [arXiv:hep-th/0503125]

View on Pith Pith review arXiv 2005
[40]

R. Kallosh, A.K. Kashani-Poor and A. Tomasiello, “Coun ting fermionic zero modes on M5 with ﬂuxes,” JHEP 0506, 069 (2005) [arXiv:hep-th/0503138]

View on Pith Pith review arXiv 2005
[41]

E. Bergshoeﬀ, R. Kallosh, A.K. Kashani-Poor, D. Soroki n and A. Tomasiello, “An index for the Dirac operator on D3 branes with background ﬂux es,” JHEP 0510, 102 (2005) [arXiv:hep-th/0507069]

View on Pith Pith review arXiv 2005
[42]

J. Park, “D3 instantons in Calabi-Yau orientifolds wit h(out) ﬂuxes,” arXiv:hep- th/0507091

View on Pith
[43]

D. L¨ ust, S. Reﬀert, W. Schulgin and P.K. Tripathy, “Fer mion zero modes in the presence of ﬂuxes and a non-perturbative superpotential,” arXiv:hep-th/0509082

View on Pith Pith review arXiv
[44]

L. Martucci, J. Rosseel, D. Van den Bleeken and A. Van Pro eyen, “Dirac actions for D- branes on backgrounds with ﬂuxes,” Class. Quant. Grav. 22, 2745 (2005) [arXiv:hep- th/0504041]

View on Pith 2005
[45]

L. Anguelova and K. Zoubos, “Five-brane instantons vs ﬂ ux-induced gauging of isome- tries,” arXiv:hep-th/0606271

View on Pith Pith review arXiv
[46]

I. Bandos and D. Sorokin, “Aspects of D-brane dynamics i n supergravity backgrounds with ﬂuxes, kappa-symmetry and equations of motion. IIB,” a rXiv:hep-th/0607163

View on Pith Pith review arXiv
[48]

L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, “Strings On Orbifolds,” Nucl. Phys. B 261, 678 (1985); “Strings On Orbifolds. 2,” Nucl. Phys. B 274, 285 (1986). 68

View on Pith 1985
[49]

D. L¨ ust, S. Reﬀert and S. Stieberger, “Flux-induced so ft supersymmetry breaking in chiral type IIb orientifolds with D3/D7-branes,” Nucl. P hys. B 706, 3 (2005) [arXiv:hep-th/0406092]

View on Pith Pith review arXiv 2005
[50]

G. Aldazabal, A. Font, L.E. Ibanez and G. Violero, “D = 4, N = 1, type IIB orien- tifolds,” Nucl. Phys. B 536, 29 (1998) [arXiv:hep-th/9804026]

View on Pith Pith review arXiv 1998
[51]

G. Zwart, “Four-dimensional N = 1 Z(N) x Z(M) orientifol ds,” Nucl. Phys. B 526, 378 (1998) [arXiv:hep-th/9708040]

View on Pith Pith review arXiv 1998
[52]

M. Klein and R. Rabadan, “Z(N) x Z(M) orientifolds with a nd without discrete tor- sion,” JHEP 0010, 049 (2000) [arXiv:hep-th/0008173]; “D = 4, N = 1 orientifol ds with vector structure,” Nucl. Phys. B 596, 197 (2001) [arXiv:hep-th/0007087]; “Ori- entifolds with discrete torsion,” JHEP 0007, 040 (2000) [arXiv:hep-th/0002103]

View on Pith Pith review arXiv 2000
[53]

O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, “Enum erating ﬂux vacua with enhanced symmetries,” JHEP 0502, 037 (2005) [arXiv:hep-th/0411061]

View on Pith Pith review arXiv 2005
[54]

P. Berglund and P. Mayr, “Non-perturbative superpoten tials in F -theory and string duality,” arXiv:hep-th/0504058

View on Pith Pith review arXiv
[55]

P.S. Aspinwall and R. Kallosh, “Fixing all moduli for M- theory on K3 x K3,” JHEP 0510, 001 (2005) [arXiv:hep-th/0506014]

View on Pith Pith review arXiv 2005
[56]

P.G. Camara, L.E. Ibanez and A.M. Uranga, “Flux-induce d SUSY-breaking soft terms on D7-D3 brane systems,” Nucl. Phys. B 708, 268 (2005) [arXiv:hep-th/0408036]

View on Pith Pith review arXiv 2005
[57]

J. Gomis, F. Marchesano and D. Mateos, “An open string la ndscape,” JHEP 0511, 021 (2005) [arXiv:hep-th/0506179]

View on Pith Pith review arXiv 2005
[58]

P. Mayr and S. Stieberger, “Threshold corrections to ga uge couplings in orbifold com- pactiﬁcations,” Nucl. Phys. B 407, 725 (1993) [arXiv:hep-th/9303017]. 69

View on Pith Pith review arXiv 1993

Forward citations

Cited by 26 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Systematics of type IIB moduli stabilisation with odd axions
hep-th 2021-09 conditional novelty 6.0 of 10

Exact inverse Kähler metrics and master formulae for the type IIB F-term scalar potential with odd moduli are derived, and a no-scale identity is proved to survive (α')^3 corrections.
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.
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.
Supersymmetric Protection and the Swampland
hep-th 2020-03 conditional novelty 6.0 of 10

Exact vanishing of supersymmetric protected quantities in quantum gravity occurs only when the theory is an orbifold of a higher-supersymmetry theory, motivating a new Swampland conjecture.
Towards Natural Inflation in String Theory
hep-th 2014-07 conditional novelty 6.0 of 10

Two-axion natural inflation can be realized in type IIB string theory with all moduli stabilized, using Ramond-Ramond two-form axions and non-perturbative potentials from D5-brane gaugino condensation or ED3/ED1 instantons.

Show 21 more citing papers

On Fluxed Instantons and Moduli Stabilisation in IIB Orientifolds and F-theory
hep-th 2011-05 conditional novelty 6.0 of 10

World-volume flux on Euclidean D3-brane instantons can cancel the U(1) charges that prevent them from stabilising Kahler moduli in chiral Type IIB orientifolds with negative-parity two-forms.
Gravity Waves and Linear Inflation from Axion Monodromy
hep-th 2008-08 conditional novelty 6.0 of 10

Wrapped branes give closed-string axions a monodromy-extended, super-Planckian field range with a linear potential, predicting a tensor-to-scalar ratio of about 0.07.
Constraints on modular inflation in supergravity and string theory
hep-th 2008-05 accept novelty 6.0 of 10

Slow-roll inflation in supergravity moduli requires the Kähler sectional curvature along the Goldstino direction to fall below 2/[3(1+gamma)], a gamma-dependent deformation of the de Sitter vacuum condition.
D-brane Deconstructions in IIB Orientifolds
hep-th 2008-05 accept novelty 6.0 of 10

The correct D3 charge, moduli count, and flux lattice dimension for singular D7-branes in IIB orientifolds are given by the topology of an auxiliary surface that resolves the double intersection with the O7-plane.
Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds
hep-th 2007-11 conditional novelty 6.0 of 10

A chiral D-brane sector cannot be added after moduli are stabilised, because it induces a D-term potential and charged instanton zero modes; only combined F- and D-term stabilisation works, demonstrated on one swiss-c...
Axion Inflation in Type II String Theory
hep-th 2007-10 conditional novelty 6.0 of 10

Axions from vanishing two-cycles in type IIB compactifications can have near-Planckian decay constants after string world-sheet corrections, potentially enabling multi-field inflation with tensor-to-scalar ratio up to 0.14.
Lifting D-Instanton Zero Modes by Recombination and Background Fluxes
hep-th 2007-08 conditional novelty 6.0 of 10

Instanton recombination and supersymmetric three-form flux do not, in general, lift the extra Goldstino modes of non-invariant D-brane instantons, so such instantons cannot generate superpotentials except in restricted cases.
Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications
hep-th 2007-05 conditional novelty 6.0 of 10

Non-perturbative alpha' corrections depending on the NS-NS two-form survive the orientifold large-volume limit, and modularity forces the D-instanton superpotential to depend on the two-form moduli through Jacobi forms.
D-brane Instantons on the T^6/Z_3 orientifold
hep-th 2007-04 conditional novelty 6.0 of 10

A detailed string-amplitude computation shows that only the U(4) and Sp(6)xU(2) gauge theories at the Z_3 orientifold singularity get ADS superpotentials from gauge instantons, while ED3 stringy instantons generate Ma...
Jumping Through Loops: On Soft Terms from Large Volume Compactifications
hep-th 2007-04 conditional novelty 6.0 of 10

String loop corrections to the Kähler potential leave the large volume scenario's minimum and its gaugino mass prediction intact, with corrections appearing only at subleading order in the volume expansion.
Coexisting Flux String Vacua from Numerical K\"ahler Moduli Stabilisation
hep-th 2025-07 conditional novelty 5.0 of 10

Numerical scans of Type IIB compactifications find single scalar potentials containing coexisting KKLT/LVS and Kahler-uplifted/LVS minima, including AdS, Minkowski, and dS pairs.
Combining Universal and Odd RR Axions for Aligned Natural Inflation
hep-th 2014-06 conditional novelty 5.0 of 10

A two-axion alignment in large-volume type IIB orientifolds yields an effective trans-Planckian decay constant of order 8 to 11 at string coupling 0.3, with moduli stabilized.
On Classifying the Divisor Involutions in Calabi-Yau Threefolds
hep-th 2013-07 conditional novelty 5.0 of 10

A systematic scan of the Kreuzer-Skarke list identifies Calabi-Yau threefolds with h^{1,1} ≤ 4 that admit divisor-exchange or reflection involutions, yielding a catalogue of backgrounds with non-zero odd (1,1)-cohomology.
Gauge Field Production in Axion Inflation: Consequences for Monodromy, non-Gaussianity in the CMB, and Gravitational Waves at Interferometers
astro-ph.CO 2011-10 conditional novelty 5.0 of 10

Backreaction from gauge fields produced during axion inflation extends inflation by about 10 e-foldings and enhances the gravitational wave signal enough to be potentially visible at Advanced LIGO/VIRGO.
Realistic Yukawa Structures from Orientifold Compactifications
hep-th 2009-05 conditional novelty 5.0 of 10

A systematic scan of globally consistent D-brane quivers shows that only a small subset can reproduce the Standard Model Yukawa structure and neutrino masses without R-parity violation or other experimental conflicts.
Non-perturbative SQCD Superpotentials from String Instantons
hep-th 2006-12 conditional novelty 5.0 of 10

A single E2-brane instanton placed on intersecting D6-branes reproduces the Affleck-Dine-Seiberg superpotential of SQCD with Nf = Nc - 1 flavours in the field theory limit.
Gaugino Condensates and D-terms from D7-branes
hep-th 2006-09 accept novelty 5.0 of 10

The flux-induced charge of a Kähler modulus under an anomalous U(1) exactly matches the number of chiral bifundamentals from the index theorem, making the Affleck-Dine-Seiberg superpotential gauge invariant.
Flux Compactification
hep-th 2006-10 accept novelty 3.0 of 10

Fluxes through the compact extra dimensions can stabilize all of string theory's moduli and break supersymmetry, yielding a vast landscape of vacua whose statistics may explain the small cosmological constant.
D-brane Instantons in Type II String Theory
hep-th 2009-02 accept novelty 2.0 of 10

D-brane instantons provide a calculable, zero-mode-driven source of non-perturbative superpotential and other holomorphic couplings in N=1 Type II orientifold compactifications.
Les Houches Lectures on Constructing String Vacua
hep-th 2008-03 unverdicted novelty 2.0 of 10

The paper is a pedagogical review of how F-theory and type IIB flux compactifications are used to construct string vacua with stabilized moduli.
Physics of String Flux Compactifications
hep-th 2007-01 accept novelty 2.0 of 10

Fluxes stabilize string moduli and generate an astronomically large discretuum of vacua whose statistical distribution makes the observed cosmological constant generic and turns the supersymmetry breaking scale into a...

How the literature uses it

51 arXiv papers cite this in 63 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 · 41 sentences without a confident label

Builds on it 1 paper

These results were generalised in [ref] : In the presence of non-perturbative contributions to the superpotential beyond the flux-induced superpotential [Here we mean superpotential contributions by instantons which would exist already without taking into account the flux induced lifting of zero modes.], supersymmetric vacua exist also for flux of Hodge type (3,0), (1,2) and (0,3).

D-brane Instantons in Type II String Theory · E3-instantons in Type IIB orientifolds with 3-form flux · 0.80

Compares with it 1 paper

First of all, in [ref] the methods for finding flux vacua with $W_0 ≪1$ were less powerful, and the smallest value obtained was $𝒪(10^-2)$, whereas we have found examples with $W_0$ as small as[ See [ref] for a comparison of our findings to the statistical predictions of [ref] .] $10^-95$.

Small Cosmological Constants in String Theory · Introduction · 0.99

Cites it as background 19 papers

In the framework of type IIB theory this is known as $F$-term uplifting [ref] and could be originated in dynamical schemes as considered in [ref] or schemes that might require the existence of additional branes and/or anti-branes [ref] .

Mirage Pattern from the Heterotic String · Introduction · 0.90
Here the complex structure moduli and the dilaton are stabilised by three-form fluxes and the Kähler moduli by non-perturbative terms arising from D3-brane instantons and/or gaugino condensation on D7-branes (for a systematic analysis see for instance [ref] ).[In the remainder of this paper we will mainly consider D3-brane instantons.

Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds · Introduction · 0.90
The properties of possible orbifolds, such as the number of moduli and their complex structure, have been fully classified [ref] , with the $$ case being one of the most examined cases in terms of non-geometric fluxes [ref] , T duality invariance [ref] and S duality invariance [ref] .

The Generalised Geometry of Type II Non-Geometric Fluxes Under T and S Dualities · Introduction · 0.90

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] [4]

D. L¨ ust, S. Reﬀert, E. Scheidegger, S. Stieberger “Reso lved Toroidal Orbifolds and their Orientifolds,” arXiv:hep-th/0609014

View on Pith Pith review arXiv

[2] [1]

S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, “De Sitt er vacua in string theory,” Phys. Rev. D 68, 046005 (2003) [arXiv:hep-th/0301240]

View on Pith Pith review arXiv 2003

[3] [2]

C.P. Burgess, R. Kallosh and F. Quevedo, “de Sitter strin g vacua from supersymmetric D-terms,” JHEP 0310, 056 (2003) [arXiv:hep-th/0309187]

View on Pith Pith review arXiv 2003

[4] [3]

D. L¨ ust, S. Reﬀert, W. Schulgin and S. Stieberger, “Modu li stabilization in type IIB orientifolds. I,” arXiv:hep-th/0506090

View on Pith Pith review arXiv

[5] [5]

S. Reﬀert and E. Scheidegger, “Moduli stabilization in t oroidal type IIB orientifolds,” Fortsch. Phys. 54, 462 (2006) [arXiv:hep-th/0512227]

View on Pith Pith review arXiv 2006

[6] [6]

F. Gmeiner, R. Blumenhagen, G. Honecker, D. L¨ ust and T. W eigand, “One in a billion: MSSM-like D-brane statistics,” JHEP 0601, 004 (2006) [arXiv:hep-th/0510170]

View on Pith Pith review arXiv 2006

[7] [7]

S. B. Giddings, S. Kachru and J. Polchinski, “Hierarchie s from ﬂuxes in string com- pactiﬁcations,” Phys. Rev. D 66, 106006 (2002) [arXiv:hep-th/0105097]

View on Pith Pith review arXiv 2002

[8] [8]

S. Gukov, C. Vafa and E. Witten, “CFT’s from Calabi-Yau fo ur-folds,” Nucl. Phys. B 584, 69 (2000) [Erratum-ibid. B 608, 477 (2001)] [arXiv:hep-th/9906070]; T.R. Taylor and C. Vafa, “RR ﬂux on Calabi-Yau and partial sup ersymmetry break- ing,” Phys. Lett. B 474, 130 (2000) [arXiv:hep-th/9912152]; P. Mayr, “On supersymmetry breaking in string theory and it...

View on Pith Pith review arXiv 2000

[9] [9]

E. Witten, “Non-Perturbative Superpotentials In Strin g Theory,” Nucl. Phys. B 474, 343 (1996) [arXiv:hep-th/9604030]

View on Pith Pith review arXiv 1996

[10] [10]

S. Ferrara, L. Girardello and H.P. Nilles, “Breakdown O f Local Supersymmetry Through Gauge Fermion Condensates,” Phys. Lett. B 125, 457 (1983); M. Dine, R. Rohm, N. Seiberg and E. Witten, “Gluino Condensat ion In Superstring Models,” Phys. Lett. B 156, 55 (1985)

View on Pith 1983

[11] [11]

P. Breitenlohner and D.Z. Freedman, “Stability In Gaug ed Extended Supergravity,” Annals Phys. 144, 249 (1982)

View on Pith 1982

[12] [12]

B. Acharya, M. Aganagic, K. Hori and C. Vafa, “Orientifo lds, mirror symmetry and superpotentials,” arXiv:hep-th/0202208

View on Pith Pith review arXiv

[13] [13]

I. Brunner and K. Hori, “Orientifolds and mirror symmet ry,” JHEP 0411, 005 (2004) [arXiv:hep-th/0303135]

View on Pith Pith review arXiv 2004

[14] [14]

T.W. Grimm and J. Louis, “The eﬀective action of N = 1 Cala bi-Yau orientifolds,” Nucl. Phys. B 699, 387 (2004) [arXiv:hep-th/0403067]; T.W. Grimm, “The eﬀective action of type II Calabi-Yau orien tifolds,” Fortsch. Phys. 53, 1179 (2005) [arXiv:hep-th/0507153] 66

View on Pith Pith review arXiv 2004

[15] [15]

F. Denef, M.R. Douglas and B. Florea, “Building a better racetrack,” JHEP 0406, 034 (2004) [arXiv:hep-th/0404257]

View on Pith Pith review arXiv 2004

[16] [16]

F. Denef, M.R. Douglas, B. Florea, A. Grassi and S. Kachr u, “Fixing All Moduli in a Simple F-Theory Compactiﬁcation,” arXiv:hep-th/0503124

View on Pith Pith review arXiv

[17] [17]

L. G¨ orlich, S. Kachru, P.K. Tripathy and S.P. Trivedi, “Gaugino condensation and nonperturbative superpotentials in ﬂux compactiﬁcations ,” JHEP 0412, 074 (2004) [arXiv:hep-th/0407130]

View on Pith Pith review arXiv 2004

[18] [18]

D. L¨ ust, P. Mayr, S. Reﬀert and S. Stieberger, “F-theor y ﬂux, destabilization of ori- entifolds and soft terms on D7-branes,” Nucl. Phys. B 732, 243 (2006) [arXiv:hep- th/0501139]

View on Pith 2006

[19] [19]

D. L¨ ust, S. Reﬀert and S. Stieberger, “MSSM with soft SU SY breaking terms from D7-branes with ﬂuxes,” Nucl. Phys. B 727, 264 (2005) [arXiv:hep-th/0410074]

View on Pith Pith review arXiv 2005

[20] [20]

K. Choi, A. Falkowski, H.P. Nilles and M. Olechowski, “S oft supersymmetry break- ing in KKLT ﬂux compactiﬁcation,” Nucl. Phys. B 718, 113 (2005) [arXiv:hep- th/0503216]

View on Pith 2005

[21] [21]

M.J. Duﬀ, B.E.W. Nilsson and C.N. Pope, “Kaluza-Klein S upergravity,” Phys. Rept. 130, 1 (1986)

View on Pith 1986

[22] [22]

B. de Carlos, S. Gurrieri, A. Lukas and A. Micu, “Moduli s tabilisation in heterotic string compactiﬁcations,” JHEP 0603, 005 (2006) [arXiv:hep-th/0507173]

View on Pith Pith review arXiv 2006

[23] [23]

D. L¨ ust and S. Stieberger, “Gauge threshold correctio ns in intersecting brane world models,” arXiv:hep-th/0302221

View on Pith Pith review arXiv

[24] [24]

K. Choi, A. Falkowski, H.P. Nilles, M. Olechowski and S. Pokorski, “Stability of ﬂux compactiﬁcations and the pattern of supersymmetry brea king,” JHEP 0411, 076 (2004) [arXiv:hep-th/0411066]

View on Pith Pith review arXiv 2004

[25] [25]

S. P. de Alwis, “Eﬀective potentials for light moduli,” Phys. Lett. B 626, 223 (2005) [arXiv:hep-th/0506266]

View on Pith Pith review arXiv 2005

[26] [26]

H. Abe, T. Higaki and T. Kobayashi, “Remark on integrati ng out heavy moduli in ﬂux compactiﬁcation,” Phys. Rev. D 74, 045012 (2006) [arXiv:hep-th/0606095]; H.X. Yang, “On moduli stabilization scheme in type IIB ﬂux co mpactiﬁcations,” arXiv:hep-th/0608155; “Moduli stabilization in type IIB ﬂ ux compactiﬁcations,” Phys. Rev. D 73, 066006 (2006) [arXiv:hep...

View on Pith Pith review arXiv 2006

[27] [27]

R.A. Horn and C.R. Johnson “Matrix Analysis”, Cambridg e University Press, 1990

View on Pith 1990

[28] [28]

R. D’Auria, S. Ferrara and M. Trigiante, “c-map,very sp ecial quaternionic geometry and dual K¨ ahler spaces,” Phys. Lett. B 587, 138 (2004) [arXiv:hep-th/0401161]

View on Pith Pith review arXiv 2004

[29] [29]

P. Candelas and X. de la Ossa, “Moduli Space Of Calabi-Ya u Manifolds,” Nucl. Phys. B 355, 455 (1991)

View on Pith 1991

[30] [30]

J.J. Blanco-Pillado, C.P. Burgess, J.M. Cline, C. Esco da, M. Gomez-Reino, R. Kallosh, A. Linde and F. Quevedo, “Inﬂating in a better racetrack,” ar Xiv:hep-th/0603129

View on Pith Pith review arXiv

[31] [31]

J.P. Conlon, “The QCD axion and moduli stabilisation,” arXiv:hep-th/0602233. 67

View on Pith Pith review arXiv

[32] [32]

M. Marino, R. Minasian, G.W. Moore and A. Strominger, “N onlinear instantons from supersymmetric p-branes,” JHEP 0001, 005 (2000) [arXiv:hep-th/9911206]

View on Pith Pith review arXiv 2000

[33] [33]

H. Jockers and J. Louis, “The eﬀective action of D7-bran es in N = 1 Calabi-Yau orientifolds,” Nucl. Phys. B 705, 167 (2005) [arXiv:hep-th/0409098]; “D-terms and F- terms from D7-brane ﬂuxes,” Nucl. Phys. B 718, 203 (2005) [arXiv:hep-th/0502059]; H. Jockers, “The eﬀective action of D-branes in Calabi-Yau o rientifold compactiﬁca- tions,” Fortsch. Phys. 53...

View on Pith Pith review arXiv 2005

[34] [34]

M. Dine, N. Seiberg and E. Witten, “Fayet-Iliopoulos Te rms In String Theory,” Nucl. Phys. B 289, 589 (1987)

View on Pith 1987

[35] [35]

L.E. Ibanez, F. Marchesano and R. Rabadan, “Getting jus t the standard model at intersecting branes,” JHEP 0111, 002 (2001) [arXiv:hep-th/0105155]

View on Pith Pith review arXiv 2001

[36] [36]

I. Antoniadis and T. Maillard, “Moduli stabilization f rom magnetic ﬂuxes in type I string theory,” Nucl. Phys. B 716, 3 (2005) [arXiv:hep-th/0412008]

View on Pith Pith review arXiv 2005

[37] [37]

A.K. Kashani-Poor and A. Tomasiello, “A stringy test of ﬂux-induced isometry gaug- ing,” Nucl. Phys. B 728, 135 (2005) [arXiv:hep-th/0505208]

View on Pith Pith review arXiv 2005

[38] [38]

R. Kallosh and D. Sorokin, “Dirac action on M5 and M2 bran es with bulk ﬂuxes,” JHEP 0505, 005 (2005) [arXiv:hep-th/0501081]

View on Pith Pith review arXiv 2005

[39] [39]

N. Saulina, “Topological constraints on stabilized ﬂu x vacua,” Nucl. Phys. B 720, 203 (2005) [arXiv:hep-th/0503125]

View on Pith Pith review arXiv 2005

[40] [40]

R. Kallosh, A.K. Kashani-Poor and A. Tomasiello, “Coun ting fermionic zero modes on M5 with ﬂuxes,” JHEP 0506, 069 (2005) [arXiv:hep-th/0503138]

View on Pith Pith review arXiv 2005

[41] [41]

E. Bergshoeﬀ, R. Kallosh, A.K. Kashani-Poor, D. Soroki n and A. Tomasiello, “An index for the Dirac operator on D3 branes with background ﬂux es,” JHEP 0510, 102 (2005) [arXiv:hep-th/0507069]

View on Pith Pith review arXiv 2005

[42] [42]

J. Park, “D3 instantons in Calabi-Yau orientifolds wit h(out) ﬂuxes,” arXiv:hep- th/0507091

View on Pith

[43] [43]

D. L¨ ust, S. Reﬀert, W. Schulgin and P.K. Tripathy, “Fer mion zero modes in the presence of ﬂuxes and a non-perturbative superpotential,” arXiv:hep-th/0509082

View on Pith Pith review arXiv

[44] [44]

L. Martucci, J. Rosseel, D. Van den Bleeken and A. Van Pro eyen, “Dirac actions for D- branes on backgrounds with ﬂuxes,” Class. Quant. Grav. 22, 2745 (2005) [arXiv:hep- th/0504041]

View on Pith 2005

[45] [45]

L. Anguelova and K. Zoubos, “Five-brane instantons vs ﬂ ux-induced gauging of isome- tries,” arXiv:hep-th/0606271

View on Pith Pith review arXiv

[46] [46]

I. Bandos and D. Sorokin, “Aspects of D-brane dynamics i n supergravity backgrounds with ﬂuxes, kappa-symmetry and equations of motion. IIB,” a rXiv:hep-th/0607163

View on Pith Pith review arXiv

[47] [48]

L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, “Strings On Orbifolds,” Nucl. Phys. B 261, 678 (1985); “Strings On Orbifolds. 2,” Nucl. Phys. B 274, 285 (1986). 68

View on Pith 1985

[48] [49]

D. L¨ ust, S. Reﬀert and S. Stieberger, “Flux-induced so ft supersymmetry breaking in chiral type IIb orientifolds with D3/D7-branes,” Nucl. P hys. B 706, 3 (2005) [arXiv:hep-th/0406092]

View on Pith Pith review arXiv 2005

[49] [50]

G. Aldazabal, A. Font, L.E. Ibanez and G. Violero, “D = 4, N = 1, type IIB orien- tifolds,” Nucl. Phys. B 536, 29 (1998) [arXiv:hep-th/9804026]

View on Pith Pith review arXiv 1998

[50] [51]

G. Zwart, “Four-dimensional N = 1 Z(N) x Z(M) orientifol ds,” Nucl. Phys. B 526, 378 (1998) [arXiv:hep-th/9708040]

View on Pith Pith review arXiv 1998

[51] [52]

M. Klein and R. Rabadan, “Z(N) x Z(M) orientifolds with a nd without discrete tor- sion,” JHEP 0010, 049 (2000) [arXiv:hep-th/0008173]; “D = 4, N = 1 orientifol ds with vector structure,” Nucl. Phys. B 596, 197 (2001) [arXiv:hep-th/0007087]; “Ori- entifolds with discrete torsion,” JHEP 0007, 040 (2000) [arXiv:hep-th/0002103]

View on Pith Pith review arXiv 2000

[52] [53]

O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, “Enum erating ﬂux vacua with enhanced symmetries,” JHEP 0502, 037 (2005) [arXiv:hep-th/0411061]

View on Pith Pith review arXiv 2005

[53] [54]

P. Berglund and P. Mayr, “Non-perturbative superpoten tials in F -theory and string duality,” arXiv:hep-th/0504058

View on Pith Pith review arXiv

[54] [55]

P.S. Aspinwall and R. Kallosh, “Fixing all moduli for M- theory on K3 x K3,” JHEP 0510, 001 (2005) [arXiv:hep-th/0506014]

View on Pith Pith review arXiv 2005

[55] [56]

P.G. Camara, L.E. Ibanez and A.M. Uranga, “Flux-induce d SUSY-breaking soft terms on D7-D3 brane systems,” Nucl. Phys. B 708, 268 (2005) [arXiv:hep-th/0408036]

View on Pith Pith review arXiv 2005

[56] [57]

J. Gomis, F. Marchesano and D. Mateos, “An open string la ndscape,” JHEP 0511, 021 (2005) [arXiv:hep-th/0506179]

View on Pith Pith review arXiv 2005

[57] [58]

P. Mayr and S. Stieberger, “Threshold corrections to ga uge couplings in orbifold com- pactiﬁcations,” Nucl. Phys. B 407, 725 (1993) [arXiv:hep-th/9303017]. 69

View on Pith Pith review arXiv 1993