The QCD Axion and Moduli Stabilisation

Cambridge); Joseph P. Conlon (DAMTP

REVIEW

The QCD Axion and Moduli Stabilisation

Joseph P. Conlon (DAMTP, Cambridge)

High Energy Physics - Theory · Submitted 22 Feb 2006 · 41 references

Pith's verdict: A clean no-go theorem for supersymmetric moduli stabilisation with unfixed axions, plus an honest but conditional outline of a non-supersymmetric large-volume construction with f_a ~ sqrt(M_SUSY M_P).

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arXiv IDhep-th/0602233 (version 3)

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

CitationCambridge), Joseph P. Conlon (DAMTP. "The QCD Axion and Moduli Stabilisation." arXiv:hep-th/0602233 (2006). https://pith.science/paper/JZLBJFYI

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Editor's note

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Dear Colleague,

Worth a look. The paper's core result is Section 3.3: a no-go theorem that in N=1 supergravity with K(T+\bar T), a supersymmetric locus solving all F-term equations with at least one flat axion is either tachyonic in the corresponding saxion direction or has a massless modulus. The argument is short, self-contained, and I don't see a hole in it. It applies to any string compactification, and it sharpens the earlier axion anti-stabilisation observations of Banks-Dine-Gorbatov and Donoghue into a general statement. The author also discusses the loopholes — nonperturbative K corrections, D-terms, BF stability in AdS — and they are genuine. The claim that the uplift to Minkowski removes BF protection is reasonable.

The positive construction is more fragile, and the paper is honest about that. To keep a massless QCD axion in the large-volume scenario, they add a Kähler correction \delta K = \varepsilon \sqrt{\tau_2}/V + \varepsilon \sqrt{\tau_3}/V, with sign and magnitude chosen so the inverse metric diverges before the blow-up cycles collapse. The text says 'we just adjust \varepsilon phenomenologically' and the appendix only constrains the scaling form of possible corrections; it does not derive this one. The stress-test worry is right: a wrong sign or different scaling would send \tau_2 - \tau_3 to zero and the construction reduces to the unstable toy model of eq. (56). So read Section 3.4 as an existence argument conditioned on an uncalculated correction, not a demonstration. The instanton-absence assumption in Section 3.5 is also by fiat, though the tables show the constraint is mild for high string scales.

I like Section 4. The observation that f_a ~ M_s ~ M_P/\sqrt{V} while m_soft ~ M_P/V, giving f_a ~ \sqrt{M_SUSY M_P}, is simple and likely to survive. It is not fitted; it follows from the volume scalings. The allowed window then points to an intermediate string scale, which is a nice phenomenological link.

Citation practice looks fine: prior work [8,9] is credited, the LVS papers are the author's own but relevant and cited where needed. No sign of overclaiming except the abstract says 'demonstrate' where the body says 'outline'. Minor.

Who is this for: string phenomenologists working on axions, moduli stabilisation, or the strong CP problem. The no-go theorem is the durable piece; the construction is a roadmap. I'd send it to a serious referee: the theorem deserves scrutiny, and the construction's assumptions should be flagged for the author to defend. My own verdict would be publish with the abstract toned down and the \varepsilon-dependence made explicit.

Would I cite it? Yes, the no-go theorem and the f_a relation.

Referee report

Significance

The no-go theorem is a clean, self-contained N=1 supergravity argument that does not depend on the details of a particular string construction; if correct, it rules out a large class of supersymmetric moduli-stabilisation attempts with massless axions and is relevant to many models in the literature. The relation f_a ~ sqrt(M_SUSY M_P) is a parameter-free consequence of the large-volume setup and is falsifiable. The instanton tables give a useful quantitative estimate of the axion-quality problem. The positive nonsupersymmetric construction is not established at the same standard: it depends on an uncalculated Kähler correction with a hand-adjusted coefficient and on the assumed absence of instantons with two or four fermionic zero modes. The manuscript is explicit about these limitations, but they mean the paper is stronger as a no-go analysis plus a proposed route than as a demonstrated construction of a viable axion vacuum.

Major objections (3)

[Section 3.4, Eq. (58)] The existence of the nonsupersymmetric vacuum is not established because it depends on the Kähler correction δK = ε√τ2/V + ε√τ3/V having the sign and magnitude needed to prevent the blow-up cycles from collapsing. The text states that ε is adjusted phenomenologically and that the actual correction would be very hard to calculate, and Appendix A only rules out certain other forms by large-volume scaling arguments; it does not show that the correction (58) is generated in any concrete compactification. If the true correction has the opposite sign or a different scaling, the τ2−τ3 direction runs away and the construction reduces to the unstable potential of Eq. (56). This is load-bearing for the paper's central positive claim that nonsupersymmetric moduli stabilisation with an unfixed QCD axion can be realised.
[Section 3.5] The assertion that the instantons generating a potential for the would-be axion are absent is imposed 'by fiat', and no mechanism or concrete model is given to realise this suppression. This is not merely a technicality: Table 2 shows that a one-instanton superpotential correction can have magnitude comparable to or larger than the QCD-induced potential for some string scales, and the paper itself requires non-QCD contributions to be smaller than about 10^-85 M_P^4 to keep |θ| < 10^-10. Without a controlled reason for the absence of the dangerous instantons, the proposed vacuum does not yet demonstrably solve the strong CP problem.
[Section 3.4] The argument that a positive wall exists because the inverse Kähler metric diverges at finite τ2 and τ3 is qualitative: the paper does not exhibit a minimum of the full potential for any explicit choice of the adjustable parameters. The positivity of the term e^K K^{i\bar j} D_i W \overline{D_{\bar j} W} is a valid indication, but a complete demonstration of a stable minimum would require checking that the competing negative terms do not overwhelm the wall and that the volume modulus is still stabilised in the region where the corrections are under control. As written, the construction is a plausible scenario rather than a proof of existence.

Minor objections (5)

[Section 3.4, text after Eq. (56)] The sentence referring to 'the sum of the blow-up volumes τ1 + τ2' and 'the difference τ1 − τ2' appears to be a typo; in the three-modulus model the stable and unstable combinations are τ2 + τ3 and τ2 − τ3, respectively.
[Section 3.3, Eq. (47)] The phrase 'using Ki¯j = Kij' is notationally confusing: K_{i\bar j} is the Kähler metric and its inverse should be denoted K^{i\bar j}. The identity used to obtain Eq. (47) should be written out explicitly.
[Section 2.2] The text says 'There are also the model independent axions, bi' but the Kähler-modulus axions were just called model-dependent; this is inconsistent and should be corrected.
[Tables 2 and 3] The tables would be easier to interpret if the assumptions m3/2 = W0/V ≈ 1 TeV and the relationship between E_UV, V and m3/2 were stated in the table captions rather than only in the surrounding text.
[Title page and abstract] There are several typographical errors ('Cam bridge', 't he', 'suﬃciently', 'fa ∼ √MSU SY MP') that should be cleaned up in a revision.

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The paper

The paper claims

A QCD axion can coexist with stabilised string moduli only if supersymmetry is broken by the moduli potential, and then the axion decay constant is forced to the geometric mean of the Planck mass and the supersymmetry-breaking scale.

The reading

This paper asks whether string theory can produce a QCD axion—the particle that solves the strong CP problem—while also stabilising the moduli that describe the extra dimensions. It argues that the simplest moduli-stabilisation schemes assign every candidate axion a mass far above the QCD scale, and it proves a no-go theorem: in any N=1 supergravity with a flat axionic direction, a supersymmetric F-term minimum cannot be stable, because the companion size modulus is necessarily tachyonic (or, in a non-generic W=0 case, massless). The paper then shows that nonsupersymmetric minima with a massless axion can nevertheless be built within large-volume IIB flux compactifications, at the cost of a specific Kähler correction and the absence of dangerous instantons. Finally, it derives a sharp numerical relation: $f_a \approx \sqrt{M_{\rm SUSY} M_P}$, which for TeV-scale supersymmetry breaking places $f_a$ inside the allowed $10^9$–$10^{12}$ GeV window.

What carries the argument

The load-bearing object is the F-term scalar potential of N=1 supergravity, $V=e^K(K^{i\bar j}D_iW\,\overline{D_jW}-3|W|^2)$, together with the holomorphy of the superpotential. The no-go theorem turns on the observation that a Peccei-Quinn shift symmetry forces $K$ to depend on $T+\bar T$ while the axion is the imaginary part of $T$; a flat axionic direction then forces $W$ to be independent of that $T$, and the identity $\partial_{\tau_u}^2 V = -4 e^K|W|^2 K_{u\bar u}$ makes the size direction tachyonic. On the constructive side, the machinery is the exponentially large volume minimum of the $\alpha'^3$-corrected Kähler potential, stabilised by the competition between the nonperturbative superpotential and the $\xi/V^3$ correction; a subleading Kähler correction $\delta K = \epsilon\sqrt{\tau_2}/V+\epsilon\sqrt{\tau_3}/V$ creates a positive wall that stops the blow-up cycles from collapsing. The final relation $f_a = \sqrt{M_P m_{\rm soft}}$ follows from the volume scalings $f_a\sim M_P/\sqrt{V}$ and $m_{\rm soft}\sim M_P/V$.

Extended reading notes

Core claim

On the paper's own terms, the central result is a split verdict. First, a general no-go theorem: no supersymmetric minimum of the F-term potential can coexist with a flat axionic direction and fully stabilised moduli. If the axion $b_u$ is unfixed, holomorphy forces the superpotential to be independent of $T_u$, and then $D_{T_u}W=0$ forces either $\partial_{T_u}K=0$ or $W=0$; in the generic case the second derivative along the size modulus is $\partial_{\tau_u}^2 V = -4 e^K |W|^2 K_{u\bar u} < 0$, making that direction tachyonic, and even if the Breitenlohner-Freedman bound makes this stable in AdS, the required uplift to Minkowski space removes that protection. Second, the no-go can be bypassed: nonsupersymmetric minima with a massless axion exist in the exponentially large volume compactifications, provided a Kähler correction of the form $\delta K = \epsilon\sqrt{\tau_2}/V + \epsilon\sqrt{\tau_3}/V$ prevents the blow-up cycles from collapsing and provided instantons with two or four fermionic zero modes are absent on the QCD cycle. Third, in those vacua the axion decay constant is set by the volume, $f_a \sim M_P/\sqrt{V}$, while soft masses are $m_{\rm soft}\sim M_P/V$, so $f_a = \sqrt{M_P\, m_{\rm soft}}$—the geometric mean of the Planck scale and the supersymmetry-breaking scale.

Load-bearing premise

The proposed massless-axion vacuum depends on the existence of a specific Kähler correction of the form $\delta K = \epsilon\sqrt{\tau_2}/V + \epsilon\sqrt{\tau_3}/V$ having the right sign and magnitude to stop the blow-up cycles from collapsing, and on the complete absence of instantons with two or four fermionic zero modes on the QCD cycle; the paper adjusts $\epsilon$ phenomenologically and assumes the instanton absence by fiat.

Editorial extensions

If this is right

Supersymmetric AdS constructions such as the KKLT scenario cannot hide a QCD axion in a flat direction: after uplift, the tachyonic Kähler modulus either destabilises the vacuum or produces an unobserved fifth force.
A surviving QCD axion forces the moduli potential to break supersymmetry, biasing string model building toward gravity mediation and intermediate string scales.
In large-volume compactifications the axion decay constant is set by the volume; to land in the allowed window, the internal volume must be exponentially large rather than string-sized.
The relation $f_a \approx \sqrt{M_{\rm SUSY} M_P}$ predicts that TeV-scale supersymmetry breaking comes with $f_a \sim 10^{10}$ GeV, placing the axion in the range targeted by direct dark-matter searches.
Higher-order instanton corrections on the QCD cycle must be absent or suppressed below $10^{-85} M_P^4$ for the axion to solve strong CP; the paper's tables give the precise bounds as a function of the string scale.

Reading between the lines

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

The no-go theorem is stated in N=1 supergravity language and therefore also constrains axions in IIA flux compactifications and heterotic models; a systematic scan of known vacuum constructions could quantify just how few string vacua admit a QCD axion.
If low-energy supersymmetry is discovered with soft masses around the TeV scale, the relation $f_a \approx \sqrt{M_P m_{\rm soft}}$ becomes a testable target: an axion search with sensitivity near $10^{10}$ GeV would either corroborate these large-volume vacua or force a different mechanism.
The required Kähler correction, while phenomenologically adjusted here, is of the form expected from loop corrections computed in toroidal examples; computing it explicitly for a concrete Calabi-Yau orientifold would turn the construction from an existence proof into a predictive model.
The same argument applies to any exactly massless axion-like particle, not just the QCD axion, suggesting that string-derived ALPs in stabilised vacua are either heavy or require special geometric conditions.

Original abstract

We investigate the conditions for a QCD axion to coexist with stabilised moduli in string compactifications. We show how the simplest approaches to moduli stabilisation give unacceptably large masses to the axions. We observe that solving the F-term equations is insufficient for realistic moduli stabilisation and give a no-go theorem on supersymmetric moduli stabilisation with unfixed axions applicable to all string compactifications and relevant to much current work. We demonstrate how nonsupersymmetric moduli stabilisation with unfixed axions can be realised. We finally outline how to stabilise the moduli such that f_a is within the allowed window 10^9 GeV < f_a < 10^{12} GeV, with f_a ~ \sqrt{M_{SUSY} M_P}.

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, 4,355 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.39 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.78 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We investigate the conditions for a QCD axion to coexist with stabilised moduli in string compactifications. We show how the simplest approaches to moduli stabilisation give unacceptably large masses to the axions. We observe that solving the F-term equations is insufficient for realistic moduli stabilisation and give a no-go theorem on supersymmetric moduli stabilisation with unfixed axions applicable to all string compactifications and relevant to much current work. We demonstrate how nonsupersymmetric moduli stabilisation with unfixed axions can be realised. We finally outline how to stabilise the moduli such that f_a is within the allowed window 10^9 GeV < f_a < 10^{12} GeV, with f_a ~ \sqrt{M_{SUSY} M_P}.

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 investigate the conditions for a QCD axion to coexist with stabilised moduli in string compactifications.	contribution 0.74	0.83	0.05	unclear 0.54
s1	We show how the simplest approaches to moduli stabilisation give unacceptably large masses to the axions.	result 0.98	0.86	0.11	asserted 1.00
s2	We observe that solving the F-term equations is insufficient for realistic moduli stabilisation and give a no-go theorem on supersymmetric moduli stabilisation with unfixed axions applicable to all string compactifications and relevant to much current work.	result 0.85	0.91	0.60	asserted 1.00
s3	We demonstrate how nonsupersymmetric moduli stabilisation with unfixed axions can be realised.	contribution 0.69	0.91	0.18	asserted 0.99
s4	We finally outline how to stabilise the moduli such that f_a is within the allowed window 10^9 GeV < f_a < 10^{12} GeV, with f_a ~ \sqrt{M_{SUSY} M_P}.	result 0.51	0.88	0.35	asserted 0.86

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v3

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

References

Works cited (41)

[1]

P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. P hys. B 258, 46 (1985)

View on Pith 1985
[2]

V. Braun, Y. H. He, B. A. Ovrut and T. Pantev, arXiv:hep-th/05 05041

View on Pith
[3]

R. Blumenhagen, M. Cvetic, P. Langacker and G. Shiu, arXiv:hep-th/0502005

View on Pith Pith review arXiv
[4]

G. Aldazabal, L. E. Ibanez, F. Quevedo and A. M. Uranga, JHEP 0008 (2000) 002 [arXiv:hep-th/0005067]

View on Pith Pith review arXiv 2000
[5]

H. Verlinde and M. Wijnholt, arXiv:hep-th/0508089. 34

View on Pith Pith review arXiv
[6]

R. D. Peccei and H. R. Quinn, Phys. Rev. D 16, 1791 (1977); R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977)

View on Pith 1977
[7]

M. Dine, arXiv:hep-ph/0011376

View on Pith Pith review arXiv
[8]

T. Banks, M. Dine and E. Gorbatov, JHEP 0408 (2004) 058 [arXiv:hep-th/0309170]

View on Pith Pith review arXiv 2004
[9]

J. F. Donoghue, Phys. Rev. D 69, 106012 (2004) [Erratum-ibid. D 69, 129901 (2004)] [arXiv:hep-th/0310203]

View on Pith Pith review arXiv 2004
[10]

V. Balasubramanian, P. Berglund, J. P. Conlon and F. Quevedo, JHEP 0503, 007 (2005) [arXiv:hep-th/0502058]

View on Pith Pith review arXiv 2005
[11]

J. P. Conlon, F. Quevedo and K. Suruliz, JHEP 0508, 007 (2005) [arXiv:hep-th/0505076]

View on Pith Pith review arXiv 2005
[12]

T. Banks and M. Dine, Nucl. Phys. B 505 (1997) 445 [arXiv:hep-th/9608197]

View on Pith Pith review arXiv 1997
[13]

T. Banks, M. Dine and M. Graesser, Phys. Rev. D 68 (2003) 075011 [arXiv:hep-ph/0210256]

View on Pith Pith review arXiv 2003
[14]

M. Endo, K. Hamaguchi and F. Takahashi, arXiv:hep-ph/06020 61

View on Pith
[15]

S. Nakamura and M. Yamaguchi, arXiv:hep-ph/0602081

View on Pith Pith review arXiv
[16]

J. Polchinski, Phys. Rev. Lett. 75, 4724 (1995) [arXiv:hep-th/9510017]

View on Pith Pith review arXiv 1995
[17]

T. W. Grimm and J. Louis, Nucl. Phys. B 699, 387 (2004) [arXiv:hep-th/0403067]

View on Pith Pith review arXiv 2004
[18]

H. Jockers and J. Louis, Nucl. Phys. B 718, 203 (2005) [arXiv:hep-th/0502059]

View on Pith Pith review arXiv 2005
[19]

T. Banks, D. B. Kaplan and A. E. Nelson, Phys. Rev. D 49, 779 (1994) [arXiv:hep-ph/9308292]

View on Pith Pith review arXiv 1994
[20]

B. de Carlos, J. A. Casas, F. Quevedo and E. Roulet, Phys. Let t. B 318, 447 (1993) [arXiv:hep-ph/9308325]

View on Pith Pith review arXiv 1993
[21]

S. B. Giddings, S. Kachru and J. Polchinski, Phys. Rev. D 66, 106006 (2002) [arXiv:hep-th/0105097]

View on Pith Pith review arXiv 2002
[22]

S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, Phys. Rev. D 68, 046005 (2003) [arXiv:hep-th/0301240]

View on Pith Pith review arXiv 2003
[23]

S. Gukov, C. Vafa and E. Witten, Nucl. Phys. B 584, 69 (2000) [Erratum- ibid. B 608, 477 (2001)] [arXiv:hep-th/9906070]. 35

View on Pith Pith review arXiv 2000
[24]

E. Witten, Nucl. Phys. B 474, 343 (1996) [arXiv:hep-th/9604030]

View on Pith Pith review arXiv 1996
[25]

F. Denef and M. R. Douglas, JHEP 0405 (2004) 072 [arXiv:hep-th/0404116]

View on Pith Pith review arXiv 2004
[26]

K. Becker, M. Becker, M. Haack and J. Louis, JHEP 0206 (2002) 060 [arXiv:hep-th/0204254]

View on Pith Pith review arXiv 2002
[27]

G. von Gersdorﬀ and A. Hebecker, Phys. Lett. B 624 (2005) 270 [arXiv:hep-th/0507131]

View on Pith Pith review arXiv 2005
[28]

M. Berg, M. Haack and B. Kors, arXiv:hep-th/0508171

View on Pith Pith review arXiv
[29]

B. C. Allanach, F. Quevedo and K. Suruliz, arXiv:hep-ph/051208 1

View on Pith
[30]

K. Choi, A. Falkowski, H. P. Nilles and M. Olechowski, Nucl. Phys. B 718, 113 (2005) [arXiv:hep-th/0503216]; K. Choi, K. S. Jeong and K. i. Ok umura, JHEP 0509 (2005) 039 [arXiv:hep-ph/0504037]; M. Endo, M. Yamaguchi and K. Yoshioka, Phys. Rev. D 72, 015004 (2005) [arXiv:hep-ph/0504036]

View on Pith Pith review arXiv 2005
[31]

P. Breitenlohner and D. Z. Freedman, Annals Phys. 144 (1982) 249

View on Pith 1982
[32]

O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, JHEP 0502 (2005) 037 [arXiv:hep-th/0411061]

View on Pith Pith review arXiv 2005
[33]

G. Villadoro and F. Zwirner, JHEP 0506 (2005) 047 [arXiv:hep-th/0503169]; G. Villadoro and F. Zwirner, arXiv:hep-th/0602120

View on Pith Pith review arXiv 2005
[34]

O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, JHEP 0507 (2005) 066 [arXiv:hep-th/0505160]

View on Pith Pith review arXiv 2005
[35]

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

View on Pith Pith review arXiv 2004
[36]

D. Lust, S. Reﬀert and S. Stieberger, Nucl. Phys. B 706, 3 (2005) [arXiv:hep-th/0406092]

View on Pith Pith review arXiv 2005
[37]

P. G. Camara, L. E. Ibanez and A. M. Uranga, Nucl. Phys. B 708, 268 (2005) [arXiv:hep-th/0408036]

View on Pith Pith review arXiv 2005
[38]

C. P. Burgess, L. E. Ibanez and F. Quevedo, Phys. Lett. B 447 (1999) 257 [arXiv:hep-ph/9810535]

View on Pith Pith review arXiv 1999
[39]

M. R. Douglas, JHEP 0305 (2003) 046 [arXiv:hep-th/0303194]

View on Pith Pith review arXiv 2003
[40]

F. Denef and M. R. Douglas, arXiv:hep-th/0602072

View on Pith Pith review arXiv
[41]

M. Berg, M. Haack and B. Kors, JHEP 0511 (2005) 030 [arXiv:hep-th/0508043]. 36

View on Pith Pith review arXiv 2005

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hep-th 2025-07 conditional novelty 6.0 of 10

Normalized divisor volumes in toric Calabi-Yau threefolds appear universal, and a GOE level-spacing model with a fitted mean reproduces axion statistics across the Kreuzer-Skarke axiverse.
String Theory and Grand Unification Suggest a Sub-Microelectronvolt QCD Axion
hep-ph 2025-05 conditional novelty 6.0 of 10

String-theoretic axions consistent with grand unification and proton decay are predicted to have masses in the 3e-11 to 1e-8 eV window, with at most 47 axions in the Kreuzer-Skarke ensemble.
Forecast constraints on the axion-photon coupling from interstellar medium heating
hep-ph 2025-01 conditional novelty 6.0 of 10

Axion dark matter resonantly heats interstellar plasma when its mass matches the plasma frequency, yielding forecast upper limits on the axion-photon coupling g as strong as about 2e-14 GeV^-1 for a 1 microgauss field.
Time-delayed gamma-ray signatures of heavy axions from core-collapse supernovae
hep-ph 2024-12 conditional novelty 6.0 of 10

No gamma-ray excess from four supernovae in Fermi-LAT data yields the strongest constraints yet on MeV-to-GeV heavy axions coupled to both QED and QCD.
QCD Axion Dark Matter from level crossing with refined adiabatic condition
hep-ph 2024-12 conditional novelty 6.0 of 10

Adiabatic level crossing between a QCD axion and an ALP can convert ALP dark matter into QCD axion dark matter, and a beat-frequency-based adiabatic condition maps the viable parameter region.
De Sitter space constraints on brane tensions and couplings
hep-th 2024-11 conditional novelty 6.0 of 10

The Festina Lente bound on particle masses is generalized to p-branes with world-volume Chern-Simons couplings, giving tension bounds in de Sitter space that string theory D-branes satisfy.
Highly Excited Electron Cyclotron for QCD Axion and Dark-Photon Detection
hep-ph 2024-10 unverdicted novelty 6.0 of 10

Proposes resonant detection of QCD axions (0.1-2.3 meV) and dark photons (down to epsilon ~2e-16) via highly excited electron cyclotron states in an open-endcap Penning trap compatible with large cavities.
Glimmers from the Axiverse
hep-th 2023-09 conditional novelty 6.0 of 10

In an ensemble of 200,000 type IIB compactifications, axion-photon couplings are hierarchically suppressed by a light threshold and by kinetic isolation, leaving only a handful of axions per model potentially detectable.
Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter
hep-th 2023-05 unverdicted novelty 6.0 of 10

Computes 1PN conservative dynamics for gravitational/EM/Proca fields and 2PN for scalar, plus radiation effects from axion-photon coupling at high PN orders in binary black hole systems with dark matter.
Projected Sensitivity of DMRadio-m$^3$: A Search for the QCD Axion Below $1\,\mu$eV
hep-ex 2022-04 conditional novelty 6.0 of 10

A proposed solenoid-based lumped-element experiment projects five-year sensitivity to QCD axion dark matter over 20 to 800 neV, reaching DFSZ couplings above about 120 neV and KSVZ couplings down to about 40 neV.
Comments on classical AdS flux vacua with scale separation
hep-th 2022-02 conditional novelty 6.0 of 10

The refined Strong AdS Distance Conjecture fails for the known scale-separated AdS3 flux vacua because the required discrete higher-form symmetry is absent, and the putative dual CFT2 has no integer operator dimensions.
Superradiance in String Theory
hep-th 2021-03 conditional novelty 6.0 of 10

Black hole superradiance excludes up to about half of the sampled type IIB Calabi-Yau compactifications at the tip of the stretched Kaehler cone near 160 axions, with stellar-mass black holes driving the bound and axi...
Superradiance Exclusions in the Landscape of Type IIB String Theory
hep-th 2020-11 conditional novelty 6.0 of 10

Black hole superradiance excludes about half of a 200,000-manifold sample of type IIB Calabi-Yau compactifications at the tip of the stretched Kähler cone, and at most 7% further inside.
A Landscape of AdS Flux Vacua
hep-th 2019-08 conditional novelty 6.0 of 10

A bilinear flux-axion polynomial technique yields new branches of type IIA Calabi-Yau flux vacua, including a tachyon-free non-supersymmetric AdS branch.
Axion superradiance in rotating neutron stars
hep-ph 2019-04 conditional novelty 6.0 of 10

Axion bound states around neutron stars can superradiantly amplify by mixing with photon modes that scatter off the resistive, rotating magnetosphere, producing an exponential instability whose rate is computed pertur...
Axion Dark Matter Detection with CMB Polarization
astro-ph.CO 2019-03 accept novelty 6.0 of 10

Oscillating axion dark matter both washes out the CMB's primordial polarization and makes the entire polarization pattern wobble in phase across the sky, and Planck data already excludes axion-photon couplings above r...
Photon Masses in the Landscape and the Swampland
hep-th 2018-08 conditional novelty 6.0 of 10

Applying Swampland distance and weak gravity conjectures to Stückelberg vector masses yields a UV cutoff of order min((m M_Pl/e)^(1/2), e^(1/3) M_Pl), which rules out a Standard Model photon mass and much of the Stück...
Opening up the QCD axion window
hep-ph 2017-08 conditional novelty 6.0 of 10

Coupling the QCD axion to a slightly more strongly coupled massless dark photon triggers tachyonic dark photon production that depletes the axion density, making fa up to about 10^17 GeV viable for order-one misalignment.
Refining the boundaries of the classical de Sitter landscape
hep-th 2016-09 conditional novelty 6.0 of 10

Classical type II supergravity with parallel Op-planes and Dp-branes admits no de Sitter vacuum for p=3,7,8, and only a narrow curvature window for p=4,5,6.
Probing MeV to 90 GeV axion-like particles with LEP and LHC
hep-ph 2015-09 conditional novelty 6.0 of 10

Existing LEP Z to two-photon and three-photon data constrain axion-like particles coupled to hypercharge or to photons across the MeV to 90 GeV mass range, and a proposed LHC three-photon search extends the reach.
Weak Gravity Strongly Constrains Large-Field Axion Inflation
hep-th 2015-06 conditional novelty 6.0 of 10

Extending the magnetic Weak Gravity Conjecture to multiple axions, plus two new conjectures about how particle masses shift across moduli space, bounds axion inflation field ranges at the Planck scale.
A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory
hep-th 2015-03 conditional novelty 6.0 of 10

A flux-scaling construction stabilizes all closed-string moduli at tree level in non-supersymmetric, tachyon-free AdS vacua, but the same scaling that makes an axion light also pushes the heavy moduli above the Kaluza...
The Challenge of Realizing F-term Axion Monodromy Inflation in String Theory
hep-th 2014-09 conditional novelty 6.0 of 10

A no-go theorem rules out the universal axion C0 as a single-field F-term axion monodromy inflaton in type IIB flux compactifications, and an explicit working example is constructed from a complex-structure axion instead.
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...
The Quest for an Intermediate-Scale Accidental Axion and Further ALPs
hep-ph 2014-03 conditional novelty 6.0 of 10

Axion and ALP photon couplings are constrained to lie on a circle in coupling space, and only models whose extra ALP carries no gluon coupling can produce the large ALP-photon coupling that the gamma-ray transparency ...
A 3.55 keV Photon Line and its Morphology from a 3.55 keV ALP Line
hep-ph 2014-03 conditional novelty 6.0 of 10

Dark matter decaying into axion-like particles, which convert to photons in cluster magnetic fields, can reproduce the 3.55 keV line and its concentration in cool-core clusters.
The 7 keV axion dark matter and the X-ray line signal
hep-ph 2014-02 conditional novelty 6.0 of 10

A 7 keV axion from string moduli, with decay constant around 10^14-15 GeV, can reproduce the 3.5 keV X-ray line while its saxion partner reheats the universe.
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.
Cosmic Axion Spin Precession Experiment (CASPEr)
hep-ph 2013-06 conditional novelty 6.0 of 10

A solid-state nuclear magnetic resonance scheme with SQUID readout could detect axion dark matter at decay constants up to 10^16 GeV, complementary to microwave cavity searches.
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...
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.
General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation
hep-th 2008-05 conditional novelty 6.0 of 10

Negative Euler number plus a blow-up cycle are argued to be necessary and sufficient for exponentially large volume moduli stabilisation, with string loop corrections lifting the remaining flat directions in fibration models.
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...
Systematics of String Loop Corrections in Type IIB Calabi-Yau Flux Compactifications
hep-th 2007-08 accept novelty 6.0 of 10

The leading string-loop correction to the Kähler potential cancels from the scalar potential at leading order whenever the correction is homogeneous of degree -2 in two-cycle volumes, an 'extended no-scale structure' ...
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.
Axions In String Theory
hep-th 2006-05 accept novelty 6.0 of 10

Across heterotic, M-theory, G2-holonomy, and D-brane compactifications, the axion decay constant is generically at or above the GUT scale, except in models where Standard Model gauge fields live on vanishing cycles.
Quality time in extra dimensions: axion quality and radion cosmology
hep-ph 2026-11 conditional novelty 5.0 of 10

A 5D circle model with a dynamical radius can keep the QCD axion high-quality while radion decay reheats the universe and dilutes the axion dark matter abundance.
Quantum Gravity Cutoff from Axions: A Type IIB Landscape Study
hep-th 2026-06 unverdicted novelty 5.0 of 10

The bound Λ_QG ≲ 2π √S f holds for C2 and C4 axions in Type IIB Calabi-Yau compactifications even near Kähler moduli space boundaries where co-scaling fails.
The Atacama Cosmology Telescope: Probing new signatures of ultralight axions with gravitational lensing
astro-ph.CO 2026-06 unverdicted novelty 5.0 of 10

New upper limits on ultralight axion dark matter fraction (<1.5% at 10^{-26} eV, <9% at 10^{-25} eV at 95% CL) from combined CMB lensing data, plus marginal 2.1σ preference at 10^{-24.5} eV driven by few points.
Sharpening the Supersymmetric Axion Weak Gravity Conjecture
hep-th 2026-05 unverdicted novelty 5.0 of 10

The paper verifies the bound fS/|n| ≤ (π/(2 κ_d)) sqrt((d-1)/(d-2)) for axion instantons and sharpens it to fS/|n| ≤ (1/κ_4) sqrt(7/2) for supersymmetric 4d instantons using three approaches in the string landscape.
Long-lived sterile neutrinos from axionlike particles at the Super Tau-Charm Facility
hep-ph 2026-05 unverdicted novelty 5.0 of 10

STCF can reach |V_eN|^2 values one to two orders of magnitude below current bounds for heavy neutral leptons via displaced-vertex searches from ALP decays in D-meson production.
Constraining F-theory Model Building with QCD Axions
hep-th 2026-05 unverdicted novelty 5.0 of 10

QCD axions constrain F-theory base threefolds to have rigid or flux-rigidified divisors, yielding typical axion masses around 10^{-9} eV and decay constants near 10^{15} GeV in allowed regions.
Boson Stars Hosting Black Holes
gr-qc 2025-11 unverdicted novelty 5.0 of 10

Numerical and analytic modeling of boson star-black hole systems in the nonrelativistic limit, with Fisher analysis indicating LISA sensitivity to ultralight dark matter mass and self-coupling via gravitational wave d...
Completing Axion Double Level Crossings
hep-ph 2025-08 unverdicted novelty 5.0 of 10

Double level crossings are common in multi-axion mass mixing of Z_N axions and ALPs, occurring multiple times for large N in the light axion case but prevented by excessively large or small N in light and heavy scenar...
Footprints of Axion-Like Particle in Pulsar Timing Array Data and James Webb Space Telescope Observations
hep-ph 2023-06 conditional novelty 5.0 of 10

A single axion-like-particle domain-wall sector, fitted jointly to pulsar-timing and JWST data, can account for both the nanohertz gravitational-wave background and early massive galaxy formation.
Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
hep-th 2020-11 accept novelty 5.0 of 10

Products of gauge field strengths generate global symmetries that quantum gravity cannot allow, and the need to break or gauge them explains axions, Chern-Simons terms, and brane dissolution in string theory.
Axion Cosmology with Early Matter Domination
astro-ph.CO 2018-07 conditional novelty 5.0 of 10

A pre-nucleosynthesis matter-dominated epoch lets axion miniclusters form even when inflation homogenized the axion field, provided the reheating temperature is below about 60 MeV, and raises the typical minicluster m...

See all 88 Pith citations

How later papers used it

203 later papers cite it

Evidence: some. 193 of the citing papers share no author with it, and 4 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 282 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 2 papers with this label

Showed that tachyons can be avoided in most instances in the simplest LVS set-up with an arbitrary number of odd moduli, which it contrasted with this paper's tachyonic no-go for SUSY minima.

Systematics of type IIB moduli stabilisation with odd axions (2021) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

191 arXiv papers cite this in 264 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 · 145 sentences without a confident label

Compares with it 2 papers

By studying the simplest LVS set-up with an arbitrary number of odd moduli, we show that tachyons can be avoided in most instances which needs to be contrasted with the tachyonic no-go of [ref] for SUSY minima.

Systematics of type IIB moduli stabilisation with odd axions · Non-perturbative superpotentials · 0.95
The crucial difference to the setting in [ref] is that we are not stabilizing all fields supersymmetrically, i.e. supersymmetry is spontaneously broken in the $T$ direction and so the argument of [ref] does not apply in our case.

A sufficient condition for de Sitter vacua in type IIB string theory · Moduli masses · 0.88

Cites it as support 1 paper

As emphasized in [ref] , this requires that they obtain a mass primarily from Kähler potential effects, rather than nonperturbative superpotential terms.

Extra-Dimensional Axion Expectations · Outlook · 0.97

Cites it as background 106 papers

Starting from the ten-dimensional low energy Lagrangian of the heterotic string [ref] , and reducing to four dimensions by compactifying a six-dimensional manifold $Z$ whose volume is $V_Z$, an effective Lagrangian describing the field $ϕ= a/f_a$ is found to be [ref] : = f_a^2/2$∂^μϕ$$∂_μϕ$ - Λ_a^4/2ϕ^2, where, in various string compactification models [ref] , the axion decay constant satisfies $f_a ≲x/S$, with $x$ a factor of $O(1)$ [For example, $x=√(2)/2$ in the context of the model-independent heterotic string.] and $S$ is the (dimensionless) action of the instantons that break the axion shift symmetry, generating the axion potential.

Cosmological window onto the string axiverse and the supersymmetry breaking scale · Axions in string theory · 0.86
We show the so-called KKLT model [ref] with [equation] where $W_0 ≪1$.

Note on moduli stabilization, supersymmetry breaking and axiverse · KKLT · 0.89
String theory and M-theory predict that there should be a large number of as-yet-undiscovered light bosonic degrees of freedom, including hidden $U(1)$ gauge fields, moduli, and axions [ref] .

Black Hole Spin Constraints on the Mass Spectrum and Number of Axion-like Fields · Introduction · 0.96

Discussion

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[1] [1]

P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. P hys. B 258, 46 (1985)

View on Pith 1985

[2] [2]

V. Braun, Y. H. He, B. A. Ovrut and T. Pantev, arXiv:hep-th/05 05041

View on Pith

[3] [3]

R. Blumenhagen, M. Cvetic, P. Langacker and G. Shiu, arXiv:hep-th/0502005

View on Pith Pith review arXiv

[4] [4]

G. Aldazabal, L. E. Ibanez, F. Quevedo and A. M. Uranga, JHEP 0008 (2000) 002 [arXiv:hep-th/0005067]

View on Pith Pith review arXiv 2000

[5] [5]

H. Verlinde and M. Wijnholt, arXiv:hep-th/0508089. 34

View on Pith Pith review arXiv

[6] [6]

R. D. Peccei and H. R. Quinn, Phys. Rev. D 16, 1791 (1977); R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977)

View on Pith 1977

[7] [7]

M. Dine, arXiv:hep-ph/0011376

View on Pith Pith review arXiv

[8] [8]

T. Banks, M. Dine and E. Gorbatov, JHEP 0408 (2004) 058 [arXiv:hep-th/0309170]

View on Pith Pith review arXiv 2004

[9] [9]

J. F. Donoghue, Phys. Rev. D 69, 106012 (2004) [Erratum-ibid. D 69, 129901 (2004)] [arXiv:hep-th/0310203]

View on Pith Pith review arXiv 2004

[10] [10]

V. Balasubramanian, P. Berglund, J. P. Conlon and F. Quevedo, JHEP 0503, 007 (2005) [arXiv:hep-th/0502058]

View on Pith Pith review arXiv 2005

[11] [11]

J. P. Conlon, F. Quevedo and K. Suruliz, JHEP 0508, 007 (2005) [arXiv:hep-th/0505076]

View on Pith Pith review arXiv 2005

[12] [12]

T. Banks and M. Dine, Nucl. Phys. B 505 (1997) 445 [arXiv:hep-th/9608197]

View on Pith Pith review arXiv 1997

[13] [13]

T. Banks, M. Dine and M. Graesser, Phys. Rev. D 68 (2003) 075011 [arXiv:hep-ph/0210256]

View on Pith Pith review arXiv 2003

[14] [14]

M. Endo, K. Hamaguchi and F. Takahashi, arXiv:hep-ph/06020 61

View on Pith

[15] [15]

S. Nakamura and M. Yamaguchi, arXiv:hep-ph/0602081

View on Pith Pith review arXiv

[16] [16]

J. Polchinski, Phys. Rev. Lett. 75, 4724 (1995) [arXiv:hep-th/9510017]

View on Pith Pith review arXiv 1995

[17] [17]

T. W. Grimm and J. Louis, Nucl. Phys. B 699, 387 (2004) [arXiv:hep-th/0403067]

View on Pith Pith review arXiv 2004

[18] [18]

H. Jockers and J. Louis, Nucl. Phys. B 718, 203 (2005) [arXiv:hep-th/0502059]

View on Pith Pith review arXiv 2005

[19] [19]

T. Banks, D. B. Kaplan and A. E. Nelson, Phys. Rev. D 49, 779 (1994) [arXiv:hep-ph/9308292]

View on Pith Pith review arXiv 1994

[20] [20]

B. de Carlos, J. A. Casas, F. Quevedo and E. Roulet, Phys. Let t. B 318, 447 (1993) [arXiv:hep-ph/9308325]

View on Pith Pith review arXiv 1993

[21] [21]

S. B. Giddings, S. Kachru and J. Polchinski, Phys. Rev. D 66, 106006 (2002) [arXiv:hep-th/0105097]

View on Pith Pith review arXiv 2002

[22] [22]

S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, Phys. Rev. D 68, 046005 (2003) [arXiv:hep-th/0301240]

View on Pith Pith review arXiv 2003

[23] [23]

S. Gukov, C. Vafa and E. Witten, Nucl. Phys. B 584, 69 (2000) [Erratum- ibid. B 608, 477 (2001)] [arXiv:hep-th/9906070]. 35

View on Pith Pith review arXiv 2000

[24] [24]

E. Witten, Nucl. Phys. B 474, 343 (1996) [arXiv:hep-th/9604030]

View on Pith Pith review arXiv 1996

[25] [25]

F. Denef and M. R. Douglas, JHEP 0405 (2004) 072 [arXiv:hep-th/0404116]

View on Pith Pith review arXiv 2004

[26] [26]

K. Becker, M. Becker, M. Haack and J. Louis, JHEP 0206 (2002) 060 [arXiv:hep-th/0204254]

View on Pith Pith review arXiv 2002

[27] [27]

G. von Gersdorﬀ and A. Hebecker, Phys. Lett. B 624 (2005) 270 [arXiv:hep-th/0507131]

View on Pith Pith review arXiv 2005

[28] [28]

M. Berg, M. Haack and B. Kors, arXiv:hep-th/0508171

View on Pith Pith review arXiv

[29] [29]

B. C. Allanach, F. Quevedo and K. Suruliz, arXiv:hep-ph/051208 1

View on Pith

[30] [30]

K. Choi, A. Falkowski, H. P. Nilles and M. Olechowski, Nucl. Phys. B 718, 113 (2005) [arXiv:hep-th/0503216]; K. Choi, K. S. Jeong and K. i. Ok umura, JHEP 0509 (2005) 039 [arXiv:hep-ph/0504037]; M. Endo, M. Yamaguchi and K. Yoshioka, Phys. Rev. D 72, 015004 (2005) [arXiv:hep-ph/0504036]

View on Pith Pith review arXiv 2005

[31] [31]

P. Breitenlohner and D. Z. Freedman, Annals Phys. 144 (1982) 249

View on Pith 1982

[32] [32]

O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, JHEP 0502 (2005) 037 [arXiv:hep-th/0411061]

View on Pith Pith review arXiv 2005

[33] [33]

G. Villadoro and F. Zwirner, JHEP 0506 (2005) 047 [arXiv:hep-th/0503169]; G. Villadoro and F. Zwirner, arXiv:hep-th/0602120

View on Pith Pith review arXiv 2005

[34] [34]

O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, JHEP 0507 (2005) 066 [arXiv:hep-th/0505160]

View on Pith Pith review arXiv 2005

[35] [35]

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

View on Pith Pith review arXiv 2004

[36] [36]

D. Lust, S. Reﬀert and S. Stieberger, Nucl. Phys. B 706, 3 (2005) [arXiv:hep-th/0406092]

View on Pith Pith review arXiv 2005

[37] [37]

P. G. Camara, L. E. Ibanez and A. M. Uranga, Nucl. Phys. B 708, 268 (2005) [arXiv:hep-th/0408036]

View on Pith Pith review arXiv 2005

[38] [38]

C. P. Burgess, L. E. Ibanez and F. Quevedo, Phys. Lett. B 447 (1999) 257 [arXiv:hep-ph/9810535]

View on Pith Pith review arXiv 1999

[39] [39]

M. R. Douglas, JHEP 0305 (2003) 046 [arXiv:hep-th/0303194]

View on Pith Pith review arXiv 2003

[40] [40]

F. Denef and M. R. Douglas, arXiv:hep-th/0602072

View on Pith Pith review arXiv

[41] [41]

M. Berg, M. Haack and B. Kors, JHEP 0511 (2005) 030 [arXiv:hep-th/0508043]. 36

View on Pith Pith review arXiv 2005