Explaining the Electroweak Scale and Stabilizing Moduli in M Theory

Bobby S. Acharya (ICTP; Gordon L. Kane; Jing Shao (MCTP; Konstantin Bobkov; Piyush Kumar; Trieste); University of Michigan)

REVIEW

Explaining the Electroweak Scale and Stabilizing Moduli in M Theory

Bobby S. Acharya (ICTP, Trieste), Konstantin Bobkov, Gordon L. Kane, Piyush Kumar, Jing Shao (MCTP, University of Michigan)

High Energy Physics - Theory · Submitted 4 Jan 2007 · 37 references

Pith's verdict: The gaugino suppression is a real, durable result; the dS uplift and the TeV gravitino are more conditional than the abstract lets on, and the paper's own Appendix A undercuts the justification for the hidden-matter Kähler assumption.

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arXiv IDhep-th/0701034 (version 3)

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CitationBobby S. Acharya (ICTP, Gordon L. Kane, Jing Shao (MCTP, Konstantin Bobkov, Piyush Kumar, Trieste), University of Michigan). "Explaining the Electroweak Scale and Stabilizing Moduli in M Theory." arXiv:hep-th/0701034 (2007). https://pith.science/paper/VMR4H62T

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Editor's note

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Two things to know up front. The tree-level gaugino mass result (eq. 264, M1/2 ≈ 0.024 m3/2) is a genuine computation that does not use the matter Kähler metric, and it survives every objection below. The de Sitter minimum and the TeV-scale gravitino are more conditional than the abstract suggests, and the paper is more candid about that in the body than in the summary sentences [abstract:s1, abstract:s3]. The classifier record says no limitations are stated; that is wrong — Sections VI A and VI D state several explicitly, and the authors deserve credit for it. Note also that the abstract's 'essentially unique' is stronger than what Section VI D actually establishes: uniqueness holds in a large-volume limit plus numerical checks, and the paper says it is not proved. That gap should be closed in revision or softened in the abstract. On the positive side, Sections III and V are clean, and the leading-order analytics are cross-checked numerically at the few-percent level (eqs. 164-165, 259-260, and 89 against 70). The anomaly-mediated cancellation in eq. 282 is striking, and the authors honestly flag that the neglected correction in eq. 283 could matter precisely because the cancellation is so tight. The stress-test concern lands, but narrowly. Appendix A derives a power-law moduli dependence for visible-sector matter at conical singularities (eq. A16), which sits awkwardly with the 'very little effect on local physics' justification offered in Section VI A. The paper does cite the appendix as further support for the assumption, but the appendix's own result is a power law, not a small effect. Whether that destabilizes the dS minimum is not shown either way — nobody has done that calculation — but it is the right place to press. It does not touch eq. 264, because the gauge kinetic function is independent of hidden matter. This is for G2/M-theory phenomenologists and anyone tracking gaugino mass predictions for the LHC. It deserves a serious referee, with the Kähler assumptions and the uniqueness claim as the main revision targets.

Referee report

Significance

If the central claims hold, this is a significant result: a fluxless M theory compactification that stabilizes the Kähler moduli, generates a hierarchy by dimensional transmutation, and yields a falsifiable prediction (suppressed, non-universal gaugino masses, light gluinos, wino-like LSP) distinguishable from Type IIB at the LHC. The gaugino-mass relation (263) is a genuinely strong result: it is independent of the Standard Model integers N_sm^i, the hidden integers N_i, the number of moduli N, and the rationals a_i. The paper also deserves credit for cross-checking its leading-order analytics against exact numerical solutions at the few-percent level (Eqs. 164–165, 259–260, 307–308), and for stating its assumptions explicitly. The phenomenological claims are, however, conditional on ansätze that are not derived from a specific G2 manifold.

Major objections (4)

[§II, Eq. (9) and discussion after Eq. (12)] The scalar potential (9) depends on the axions t_i only through the single combination cos[(b1N1 − b2N2)·t]. Extremizing with respect to the axions therefore fixes one linear combination, as the text notes after Eq. (12), leaving N−1 axion directions exactly flat in this potential. The abstract and §IX nonetheless state that 'all moduli are stabilized by the effective potential.' Either the remaining axions are lifted by effects not included here (for example, additional nonperturbative contributions or membrane instantons), in which case this should be stated and the mechanism identified, or the 'all moduli' claim needs to be qualified. This is load-bearing for the paper's headline result.
[§VI A vs. Appendix A, Eq. (A16)] Section VI A assumes a canonical, moduli-independent Kähler metric for the hidden-sector mesons, justified by the observation that chiral fermions sit at point-like conical singularities where 'the bulk moduli s_i should have very little effect on the local physics.' Appendix A, however, derives for visible-sector chiral matter at exactly such singularities a power-law dependence K̃_α = ∏(Γ(1−θ_αi)/Γ(θ_αi))^{1/2} with tan(πθ_αi) = c_αi (s_i)^l and l rational O(1) (Eq. A16). The same localization argument is used to justify both conclusions, yet they differ. If the hidden meson metric carries the same (s_i)^l dependence, the meson F-term (100) and the scalar potential (104) acquire moduli-dependent prefactors, and neither the dS minimum of §VI C nor the leading-order cancellation behind Eq. (264) is guaranteed to survive. The authors acknowledge the derivation is an open problem, but do not confront the tension with their own Appendix. A concrete test would be to redo §VI C with the metric of Eq. (A16) and check whether the dS minimum and the 0.024 coefficient persist.
[§VII D, Eqs. (191)–(199)] The claim that a small cosmological constant 'automatically' pushes m3/2 to 1–100 TeV rests on the assumed flat measure over (P, Q−P, N) with P ≤ 100, Q ≤ 100, C2 = 1, and on the observation, stated explicitly in §VII D, that 'the peak ... is entirely due to the smallest possible value (Q−P)_min = 3,' which yields the suppression e^{−28} of Eq. (208). This is a statement about the prior, not about the dynamics. Moreover, from Eq. (198), m3/2 ∝ V_X^{−3/2}, so the O(100) TeV peak corresponds to V_X of order unity, i.e., the boundary of the supergravity regime (s_i > 1) on which the whole analysis rests. The abstract's 'automatically' overstates what is shown. A concrete test would be to repeat the scan with a different measure (for example, logarithmic in V_X, or weighted by the number of G2 manifolds) and to show that the peak survives, or to argue that (Q−P) = 3 is dynamically preferred.
[§VI D, Eqs. (149)–(152)] The 'essentially unique dS vacuum' result is established only in the large associative-cycle limit (T_A large, ỹ → 0, w̃ → −∞) and by treating δ of Eq. (150) as a continuous deformation parameter independent of A, a step the text itself flags as questionable ('One may object to this proposition ...'). The abstract states uniqueness without this qualification. Since uniqueness is one of the paper's headline results, either the approximation should be stated in the abstract and conclusions, or the argument should be extended beyond leading order in 1/T_A.

Minor objections (7)

[Eq. (69)] The line reads 's(2)2 = 13.59, s(2)2 = 13.59', repeating the same index; presumably the first should be s(2)1.
[Eq. (88)] The approximate coefficients '∼0.143 N2' and '∼0.016 N1' appear to have N1 and N2 interchanged relative to the denominators in the preceding lines.
[Fig. 3 caption and Fig. 4 text] The captions read 'N1i = {1,2,2}, N1i = {3,3,4}' and 'N1i = {1,0,1}, N1i = {1,1,1}'; the second occurrence in each pair should presumably be N2i.
[§VIII D, §VIII F, §IX] The REWSB and wino dark matter claims are asserted and deferred to Ref. [13], listed as 'To Appear.' Since they appear in the conclusions, either summarize the calculation here or soften the wording.
[§VIII F] The statement that 'the lightest neutralino is a good dark matter candidate' sits uneasily with the preceding sentence that the thermal wino relic density is 'very small'; clarify that the claim relies on non-thermal production.
[Eq. (154)] State explicitly that the quoted AdS vacuum energy is for the specific toy parameters of Eq. (67), not a generic prediction.
[§VII C] The assumptions ρ ≤ 10, P,Q ≤ 30, C2 = 1, and the flat measure should be collected in one place and flagged as inputs, since the quoted fractions Δ depend on them.

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The paper

The paper claims

In M theory compactified on a seven-dimensional manifold of G2 holonomy with no fluxes, strong gauge dynamics in two hidden sectors is enough to stabilize every modulus and to generate a metastable de Sitter vacuum whose vacuum energy can,

The reading

The paper asks whether the weak scale can come out of M theory rather than being put in by hand. Its answer is that in fluxless compactifications on manifolds of G2 holonomy, the entire effective potential is non-perturbative — it comes from gaugino condensation in hidden gauge sectors — and therefore depends on all the moduli at once, so the same dynamics that generates a small scale also pins the geometry. The authors solve the resulting potential explicitly for two hidden sectors, find isolated supersymmetric and supersymmetry-breaking anti-de Sitter vacua with all moduli fixed, and then show that adding chiral matter to one hidden sector supplies a positive F-term contribution that turns the deepest of these into a metastable de Sitter minimum. That de Sitter vacuum is argued to be essentially unique for a given manifold, and it is reached without anti-branes or any other explicit supersymmetry-breaking uplift. The payoff claimed is twofold: tree-level gaugino masses come out suppressed by roughly a factor of forty relative to the gravitino, and imposing a small cosmological constant pushes the gravitino mass — and with it all superpartner masses — into the 1 to 100 TeV range.

What carries the argument

The mechanism is dimensional transmutation operating on the full moduli space. Because the Peccei-Quinn shift symmetries of the axions forbid a perturbative superpotential, every term in $W$ is exponentially small, $e^{-b_k N_{ki} s^i}$, and the scalar potential $V = e^{K}(K^{i j} F_i F_j - 3|W|^2)$ with $K = -3 ln(4 pi^{1/3} V_X)$, $V_X = prod s_i^{a_i}$, $sum a_i = 7/3$, is a sum of exponentials in the moduli. Extremizing with respect to the axions fixes one linear combination and forces a relative sign; extremizing with respect to the saxions gives a system that can be recast, via an auxiliary variable $alpha$, into linear equations for the $s_i$ plus a single transcendental constraint, which is what makes the $N$-modulus problem tractable. The same exponential structure is what suppresses the gaugino mass: the moduli $F$-terms vanish at leading order near the would-be supersymmetric point, so $M_{1/2}$ is controlled by the first subleading term, which carries an inverse power of the associative three-cycle volume — equivalently a power of the hidden-sector gauge coupling at unification.

Extended reading notes

Core claim

The central claim is that a single non-perturbative superpotential, $W = A_1 e^{i b_1 f_1} + A_2 e^{i b_2 f_2}$ with gauge kinetic functions $f_k = N_{ki} z^i$ linear in the moduli, stabilizes all $N = b_3(X)$ moduli of a fluxless G2 compactification. Solving the $F_i = 0$ conditions reduces to $N$ linear equations plus one transcendental constraint, and the solutions are isolated. When the two hidden sectors share a gauge kinetic function, the supersymmetric vacuum has a closed approximate form, $s_i = a_i N_i^{-1} (3PQ/14)$-type expressions with $PQ/(P-Q) - Q) - Q$, and the non-supersymmetric vacua organize into $2^N$ branches labelled by a parameter $A = (3/7) m_k a_k$; only the branches with all $s_i > 1$ survive the supergravity regime. Adding one hidden-sector meson $Q = (2Q Q)^{1/2}$ with a Seiberg-type superpotential $A_1 Q^{a} e^{i b_1 f} + A_2 e^{i b_2 f}$, $a = -2/(N_c - N_f)$, gives a matter $F$-term that does not cancel against $-3|W|^2$ and produces a de Sitter minimum when $Q - P > 2$. The authors argue this de Sitter vacuum is unique: for $A < 1$ the deformation of the coupled system has no solution with all moduli positive once the $A = 1$ vacuum is de Sitter. From there the phenomenological claim: the tree-level MSSM gaugino mass is $M_{1/2} = -(2 L_{1,+}/3 + 1) m_{3/2}$, and after imposing the vanishing-cosmological-constant condition $P - P) - P) = 84$ (for $Q - P = 3$) this evaluates to $M_{1/2} -0.024 m_{3/2}$, while the same condition gives $m_{3/2} - 514$ TeV $/ V_X^{3/2}$ with $V_X > 1$, i.e. an upper bound of order 100 TeV.

Load-bearing premise

The whole calculation assumes a specific factorized form for the moduli Kähler potential, $K = -3 ln(4 pi^{1/3} V_X)$ with $V_X = prod s_i^{a_i}$ and $sum a_i = 7/3$, and additionally assumes that the hidden-sector matter Kähler metric is canonical and independent of the moduli — an assumption the authors state outright they cannot check, since they write that they 'cannot explicitly calculate the moduli dependence of the matter Kähler potential.'

Editorial extensions

If this is right

Every fluxless G2 compactification with at least two strongly coupled hidden sectors and the assumed volume form stabilizes all its moduli, so the moduli problem in this corner of M theory is solved by the same dynamics that generates the hierarchy.
Gaugino masses are generically a few percent of the gravitino mass across this whole class of vacua, independent of the number of moduli and of the integers defining the Standard Model gauge kinetic function.
Because the tree-level gaugino mass is so small, the anomaly-mediated contribution is comparable to it, and the two partially cancel for $SU(2)$ and $SU(3)$ — the paper quotes $M_1 = -10.2$, $M_2 = -0.84$, $M_3 = +1.35$ in units of $10^{-3} m_{3/2}$ — giving a light gluino and a wino-like lightest neutralino.
Requiring the leading vacuum energy to vanish is not an independent tuning: it fixes $P ln(A_1 Q / A_2 P)$ to a large number (84 for $Q - P = 3$), and that same number is the exponent that brings $m_{3/2}$ down to 1–100 TeV.
The eleven-dimensional Planck scale in these vacua sits between $3.6 times 10^{16}$ GeV and $4.3 times 10^{18}$ GeV, so standard gauge coupling unification survives alongside low-scale supersymmetry.

Reading between the lines

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

The uniqueness argument for the de Sitter vacuum is really an argument about the discriminant of a biquadratic in the meson vev, and it is carried out in the large-three-cycle limit where $tilde{y} -> 0$; a numerical scan at finite volume, which the authors say they performed but do not display in full, is the natural place to look for counterexamples.
If the suppression factor $M_{1/2} approx 0.024 m_{3/2}$ survives, the LHC signature is dominated by gluino pair production with a compressed, wino-like neutralino — a spectrum that would look quite unlike both the large-volume Type IIB and the KKLT patterns, so the gaugino-to-scalar mass ratio is the sharpest discriminator this class of vacua offers.
The chain that produces the TeV peak runs through a single large logarithm, so the prediction is robust against subleading corrections in a way that a direct tuning of $m_{3/2}$ would not be; that robustness is a testable structural feature, not merely a numerical coincidence.
The whole construction rests on a factorized volume $V_X = prod s_i^{a_i}$ with $sum a_i = 7/3$; if the true Kähler potential for a compact G2 manifold with the required orbifold singularities departs from this form even at moderate volume, the linear-plus-transcendental structure that makes the $N$-modulus potential solvable disappears with it.

Original abstract

In a recent paper \cite{Acharya:2006ia} it was shown that in $M$ theory vacua without fluxes, all moduli are stabilized by the effective potential and a stable hierarchy is generated, consistent with standard gauge unification. This paper explains the results of \cite{Acharya:2006ia} in more detail and generalizes them, finding an essentially unique de Sitter (dS) vacuum under reasonable conditions. One of the main phenomenological consequences is a prediction which emerges from this entire class of vacua: namely gaugino masses are significantly suppressed relative to the gravitino mass. We also present evidence that, for those vacua in which the vacuum energy is small, the gravitino mass, which sets all the superpartner masses, is automatically in the TeV - 100 TeV range.

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, 3,789 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.87 · compares with prior results 0.86 · 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.

In a recent paper \cite{Acharya:2006ia} it was shown that in $M$ theory vacua without fluxes, all moduli are stabilized by the effective potential and a stable hierarchy is generated, consistent with standard gauge unification. This paper explains the results of \cite{Acharya:2006ia} in more detail and generalizes them, finding an essentially unique de Sitter (dS) vacuum under reasonable conditions. One of the main phenomenological consequences is a prediction which emerges from this entire class of vacua: namely gaugino masses are significantly suppressed relative to the gravitino mass. We also present evidence that, for those vacua in which the vacuum energy is small, the gravitino mass, which sets all the superpartner masses, is automatically in the TeV - 100 TeV range.

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	In a recent paper \cite{Acharya:2006ia} it was shown that in $M$ theory vacua without fluxes, all moduli are stabilized by the effective potential and a stable hierarchy is generated, consistent with standard gauge unification.	background 1.00	0.04	0.09	asserted 0.98
s1	This paper explains the results of \cite{Acharya:2006ia} in more detail and generalizes them, finding an essentially unique de Sitter (dS) vacuum under reasonable conditions.	contribution 0.90	0.95	0.25	asserted 1.00
s2	One of the main phenomenological consequences is a prediction which emerges from this entire class of vacua: namely gaugino masses are significantly suppressed relative to the gravitino mass.	result 0.69	0.65	0.49	asserted 0.99
s3	We also present evidence that, for those vacua in which the vacuum energy is small, the gravitino mass, which sets all the superpartner masses, is automatically in the TeV - 100 TeV range.	result 0.98	0.86	0.18	asserted 0.73

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.81.

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

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Forward citations

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Low Energy Probes of PeV Scale Sfermions
hep-ph 2013-08 accept novelty 6.0 of 10

In mini-split supersymmetry, kaon mixing already probes PeV-scale squarks, and planned neutron-EDM, muon-to-electron, and charm-mixing measurements will reach 100 to 1000 TeV sfermion masses.
Quantum Gravity Constraints on Inflation
hep-th 2012-03 conditional novelty 6.0 of 10

Requiring the entropy of inflationary fields to be less than the de Sitter entropy yields a parametric bound on transPlanckian field ranges and constrains large-rank-gauge-group de Sitter models.
Accurate estimate of the relic density and the kinetic decoupling in non-thermal dark matter models
hep-ph 2011-04 conditional novelty 6.0 of 10

A full numerical treatment of non-thermal dark matter production from decaying moduli, plus a new formalism for kinetic decoupling in coannihilating dark matter, shows that standard equilibrium assumptions can fail at...
Non-thermal Dark Matter and the Moduli Problem in String Frameworks
hep-ph 2008-04 conditional novelty 6.0 of 10

In the G2-MSSM string framework, late-decaying moduli satisfy BBN constraints, avoid the gravitino problem, and produce wino dark matter with a relic density within a factor of a few of the observed value.

Show 16 more citing papers

The $G_2$-MSSM - An $M$ Theory motivated model of Particle Physics
hep-ph 2008-01 conditional novelty 6.0 of 10

Within the authors' G2 compactification framework, gaugino masses are suppressed by a factor of about 83 relative to the gravitino, giving heavy multi-TeV scalars, sub-TeV gauginos, and a wino-like lightest superpartner.
Black Hole Spin Constraints on the Mass Spectrum and Number of Axion-like Fields
hep-ph 2018-05 conditional novelty 5.0 of 10

Combining black-hole superradiance exclusions with statistical mass distributions rules out roughly 30 or more axion-like fields for a wide range of distribution widths and central masses.
Wino Dark Matter and Future dSph Observations
hep-ph 2014-05 conditional novelty 5.0 of 10

If the J-factor uncertainties of all eight dwarf spheroidals reach 0.1 dex, 15 years of Fermi-LAT plus 10 years of GAMMA-400 data would probe the entire 0.27 to 2.9 TeV wino mass range.
Gaugino coannihilations
hep-ph 2014-03 conditional novelty 5.0 of 10

Coannihilation between gauginos in high-scale supersymmetry lets bino or wino dark matter be as heavy as 7 to 8 TeV, well above the 3.1 TeV ceiling for pure wino dark matter.
Indirect Detection Analysis: Wino Dark Matter Case Study
astro-ph.HE 2014-01 conditional novelty 5.0 of 10

Combining seven indirect-detection channels with one-loop electroweak and Sommerfeld corrections, the authors report that Wino dark matter is excluded below about 800 GeV and between 1.8 and 3.5 TeV.
In Wino Veritas? Indirect Searches Shed Light on Neutralino Dark Matter
hep-ph 2013-07 conditional novelty 5.0 of 10

Existing gamma-ray data exclude wino dark matter from 100 GeV to 3 TeV for cuspy NFW or Einasto halos, and force moduli-decay cosmologies to reheat above about a GeV.
Supersymmetry Breaking due to Moduli Stabilization in String Theory
hep-th 2011-11 accept novelty 5.0 of 10

Strong stabilization of the string volume modulus suppresses tree-level gaugino masses by m_{3/2}/m_sigma, leaving anomaly mediation to generate a split-supersymmetry spectrum with a gravitino near 100 TeV.
Bounds on Scalar Masses in Theories of Moduli Stabilization
hep-ph 2010-06 conditional novelty 5.0 of 10

A supergravity eigenvalue bound implies at least one stabilized modulus is lighter than or comparable to the gravitino, forcing a non-thermal pre-BBN cosmology and a gravitino heavier than about 30 TeV.
A Non-thermal WIMP Miracle
astro-ph.CO 2009-08 conditional novelty 5.0 of 10

Moduli with masses of 10 to 100 TeV, the window required to solve the cosmological moduli problem, decay into WIMPs whose non-thermal freeze-out reproduces the observed dark matter density.
More about F-term uplifting
hep-th 2007-07 conditional novelty 5.0 of 10

Direct coupling between the uplifting sector and the Kähler modulus raises the modulus-to-gravitino mass ratio to O(a^2) while keeping the modulus F-term at O(m_3/2/a), preserving mirage mediation for gauginos but not...
De Sitter vs Quintessence in String Theory
hep-th 2018-08 conditional novelty 4.0 of 10

De Sitter vacua from type IIB flux compactifications are argued to be under better calculational control than string quintessence models, which require extra fine-tuning and generically couple to Standard Model fields.
Physics at a 100 TeV pp collider: beyond the Standard Model phenomena
hep-ph 2016-06 conditional novelty 4.0 of 10

Compiles projected 100 TeV reach estimates for supersymmetry, dark matter, and exotic resonances, finding multi-TeV sensitivity well beyond the LHC in nearly every channel studied.
Testing String Theory with CMB
hep-th 2007-04 conditional novelty 4.0 of 10

In KKLT-based string inflation the Hubble scale during inflation is bounded by the gravitino mass, so a TeV gravitino forces the tensor-to-scalar ratio below 10^-24, and any detection of r above 10^-3 would require gr...
On Inflation in String Theory
hep-th 2007-02 conditional novelty 4.0 of 10

A survey of string-theory inflation that also constructs a supergravity axion valley model, claimed as the first explicit realization of natural inflation in supergravity, with a stabilized radial partner and a flat a...
Midi-review: Status of weak scale supersymmetry after LHC Run 2 and ton-scale noble liquid WIMP searches
hep-ph 2020-02 conditional novelty 3.0 of 10

Combining a landscape statistical pull toward large soft SUSY terms with an anthropic bound on the weak scale yields a 125 GeV Higgs and sparticles beyond LHC reach, which the authors argue explains the null results so far.
Moduli Stabilization in String Theory
hep-th 2023-10 accept novelty 2.0 of 10

This is a review of moduli stabilization in string compactifications, organizing the KKLT and Large Volume Scenario constructions, their extensions to other string theories, and their cosmological and particle-physics...

How later papers used it

51 later papers cite it

Evidence: some. 38 of the citing papers share no author with it, and 4 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 132 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 paper by the same authors is listed below: 1 built on it and 1 used its method or tool. It appears under more than one label.

Builds on it 1 paper · 1 by the same authors

By the same authors

Redid the analysis of moduli stabilization from this paper in a much more general context.

Kahler Independence of the G2-MSSM (2008) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

Uses its method or tool 1 paper · 1 by the same authors

By the same authors

Used the techniques developed earlier in this paper to understand the minima of the potential.

Kahler Independence of the G2-MSSM (2008) (same authors) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

49 arXiv papers cite this in 130 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 · 98 sentences without a confident label

Builds on it 1 paper

Following this, we re-do the analysis of Moduli stabilization from [ref] in this much more general context.

Kahler Independence of the G2-MSSM · Introduction · 1.00

Uses its method or tool 1 paper

To understand the minima of the potential we will use the techniques developed earlier in [ref] .

Kahler Independence of the G2-MSSM · Moduli stabilization · 0.99

Uses its data or values 2 papers

The mass matrix can be written as: [equation] where $K_1$ to $K_4$ are obtained in [ref] : [equation] where $ϕ_0^2≈0.734$.

Non-thermal Dark Matter and the Moduli Problem in String Frameworks · Moduli Masses · 0.94
From [ref] we know that the moduli vevs are approximately $⟨s ⟩∼0.1 m_pl$, $⟨F_s ⟩∼m_1/2 m_pl$ and from the standard supergravity Lagrangian [ref] we get an effective $μ$-term: μ= ⟨m_3/2 K_H_u H_d - F^k K_H_u H_d k ⟩, which leads to μ∼⟨s ⟩/m_pl m_3/2 + ⟨F_s ⟩/m_pl .

SO(10) Grand Unification in M theory on a G2 manifold · $SU(5)$ · 0.97

Compares with it 4 papers

Whilst non-trivial, these modifications do not change the results of [ref] , [ref] much.

Kahler Independence of the G2-MSSM · Introduction · 0.93
These could present some relevant differences with respect to the results found in [ref] .

Type IIA/M-theory Moduli fixing in a Class of Orientifold Models · M-theory without Fluxes · 0.87
In that sense the heterotic mechanism of dilaton stabilization is somewhat similar to the one conjectured in the framework of M theory on $G_2$-manifolds (which requires a racetrack scenario and an up-lifting sector [ref] ).

Mirage Pattern from the Heterotic String · Conclusions · 0.94

Cites it as support 3 papers

This is borne out by explicit calculations, see e.g. [ref] .

The Axiverse induced Dark Radiation Problem · The Axiverse Induced Dark Radiation Problem · 0.99
The key point here is that in the compactified $M$-theory context, for a generic moduli Kähler potential the real moduli $s_i$ will all obtain vevs of the same order [ref] .

R-Parity Conservation from a Top Down Perspective · $κ/μ$ in $M$ theory Compactifications on $G_2$ Manifolds · 0.97
In fact, all the moduli can be stabilised by considering superpotentials that arise from two hidden sector contributions [ref] .

String Cosmology: from the Early Universe to Today · Moduli stabilisation in M-theory · 0.97

Cites it as background 15 papers

In the rest of this section, the results obtained in [ref] are summarized and the assumptions about the microscopic structure needed to define the framework and make contact with low energy physics are specified.

The $G_2$-MSSM - An $M$ Theory motivated model of Particle Physics · Introduction and Summary · 0.81
In a series of papers, [ref] , [ref] , [ref] , a very detailed model of moduli physics coupled to matter has been described.

Kahler Independence of the G2-MSSM · Introduction · 0.98
The subject of this note is one such framework with a UV completion, the “$G_2$-MSSM" [ref] .

Revisiting Gluinos at LHC · Introduction · 0.80

Discussion

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