Kaehler Corrections for the Volume Modulus of Flux Compactifications

Arthur Hebecker; Gero von Gersdorff

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Kaehler Corrections for the Volume Modulus of Flux Compactifications

Gero von Gersdorff, Arthur Hebecker

High Energy Physics - Theory · Submitted 14 Jul 2005 · 17 references

Pith's verdict: A short, correct dimensional-analysis note that fixes the one-loop Kähler exponent for the volume modulus; the coefficient is not computed and the paper says so.

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arXiv IDhep-th/0507131 (version 3)

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CitationArthur Hebecker, Gero von Gersdorff. "Kaehler Corrections for the Volume Modulus of Flux Compactifications." arXiv:hep-th/0507131 (2005). https://pith.science/paper/5DN7B3JJ

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Editor's note

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The thing to take away: for a no-scale volume modulus with Re T = R^α and α = sqrt(k(k+2)/3), the leading finite one-loop correction to K that cannot be absorbed into local d-dimensional operators is ΔK ~ 1/(T+T̄)^c with c = sqrt(3(k+2)/k). For type IIB (k=6) that gives c=2, so ΔK ~ 1/(T+T̄)² and a potential |W|²/R⁸. That is a clean, checkable statement, and I do not see it in the earlier literature in this general form. The 5d Scherk-Schwarz case falling out as c=3, reproducing the known R⁻⁴ Casimir, is a real consistency test rather than decoration. The algebra is short enough to redo on a napkin, and I did; the closed form is right. (The intermediate expression in Eq. (10) as I read it looks like a typo — it should be (k+2)/α — but the final formula is correct.) What the paper does well is the Brans-Dicke frame bookkeeping. Working before Weyl rescaling makes it obvious that the loop corrections are R⁻²R and R⁻⁴(∂R)², and that these are precisely the terms that cannot be written as the reduction of a local 10d operator, which is what separates them from the α' corrections of Becker et al. Soft spots, in order of weight. First, c_Casimir is not computed, and the stabilization discussion in Eqs. (15)-(17) needs its sign and size. The paper is upfront about this, but the S-duality argument that you cannot dial c_α' small is an argument by duality, not a calculation, and it is the weakest link in the large-R_min story. Second, the claim that the finite remainder is a pure function of R with an unambiguous coefficient is plausible but not demonstrated; scheme dependence of the finite part deserves a line. Third, the suggestion that large h^{1,1}, h^{2,1} with small χ makes c_Casimir large is a hope, not an estimate — fine as a proposal, but do not build on it yet. Who should read it: anyone working on loop corrections to Kähler potentials or radion stabilization in IIB. It is a useful reference for the R⁻⁸ term and for the frame bookkeeping. It is not a computation and does not claim to be. Recommendation: send it out. It is short, correct, and honest about its scope; a referee should push on the scheme-dependence point and on the S-duality argument, not on the central exponent.

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Major objections (3)

[Eqs. (6)-(10)] The derivation of the exponent c rests on the assumption that the finite one-loop correction depends only on R and is a pure function of R, so that dimensional analysis fixes F ~ 1/R² and G ~ 1/R⁴. The manuscript acknowledges this ('we have pretended that the field-theoretic one-loop corrections are finite'), but the acknowledgment is not followed by a demonstration that the finite part is scheme-independent and R-only. In particular, the coefficient of the 1/(T+T̄)^c term is not computed, and the paper does not show that no additional R-dependence (e.g., from light fields below the KK scale or from the warp factor that is explicitly neglected) enters the finite part. This is load-bearing for the central parametric claim, and a short argument or explicit statement of the regime of validity would strengthen it.
[Eqs. (15)-(17)] The stabilization proposal depends on the sign and magnitude of c_Casimir, which the paper does not compute. The minimum in Eq. (16) requires c_α' < 0 and c_Casimir > 0, and the claim in Eq. (17) that (R_min M)² ~ 1/(M⁶ α'³) is large at small α' is immediately followed by the observation that this is the strong-coupling regime, with S-duality implying the coefficient of the R⁻⁶ term can never be made small. The net effect is that the stabilization scenario is not established even parametrically. The paper is explicit that this is a proposal, but the section would benefit from stating clearly which of the two coefficients (or their ratio) would need to be computed to settle the question, and whether the S-duality argument closes off the large-R window entirely or only in the small-α' regime.
[Eq. (10) and surrounding text] The identification Re T = R^α with α = sqrt(k(k+2)/3) is used to convert the Brans-Dicke-frame kinetic correction into a Kähler correction. For the k = 6 type IIB case this gives α = 4, consistent with Re T ~ R⁴, and for k = 1 it gives α = 1. The algebra is correct, but the paper does not discuss whether the relation between Re T and R survives the inclusion of the one-loop correction itself, i.e., whether the field redefinition implicit in going to the Einstein frame commutes with the loop expansion. A brief remark on this point would help the reader assess the robustness of Eq. (10).

Minor objections (6)

[Abstract] The abstract states the result in terms of 'supergravity loop corrections' without specifying that the leading finite correction is the one that cannot be absorbed into local d-dimensional operators; adding this qualifier would align the abstract with the more careful statement in the body of the paper.
[Eq. (7) and following paragraph] The text says 'we have pretended that the field-theoretic one-loop corrections are finite' and then notes that a UV cutoff would enter otherwise. It would be clearer to state explicitly which contributions are being discarded as local d-dimensional counterterms and which are being kept as the finite prediction, since this distinction is the basis for the comparison with the α' correction.
[Eq. (11)] The numerical prefactor c(c-1) is mentioned but not derived; a one-line indication of where it comes from (the standard supergravity scalar potential formula applied to ΔK) would help the reader verify the vanishing at c = 0 and c = 1.
[Eq. (16)] The minimum in Eq. (16) is stated without showing the derivative of Eq. (15); including the intermediate step would make the algebra easier to check.
[Acknowledgements and references] Reference [17] is a talk ('String Phenomenology 2005', Munich, June 2005) cited for work in progress on explicit computation of c_Casimir; since this is unpublished, the paper should be clear that the explicit coefficient is not yet available in the literature, which it largely is but could state more directly.
[General] The paper uses both 'Brans-Dicke frame' and 'Einstein frame' throughout; a short glossary or a footnote at first use would help readers who are not familiar with the frame conventions in this literature.

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The paper

The paper claims

The leading one-loop correction to the volume modulus's Kähler potential is fixed by dimensional analysis to be $1/(T+̄T)^2$, giving a Casimir-like $|W|^2/R^8$ potential that competes with string $α'$ corrections.

The reading

In type IIB flux compactifications the complex-structure moduli and the dilaton are fixed by fluxes, but the overall volume modulus (the radion) survives as a flat direction of a no-scale model. The paper asks what one-loop supergravity corrections do to that flat direction: how they renormalise the Kähler potential, and whether the resulting potential can help stabilise the volume. The authors argue that in the frame before Weyl rescaling the corrections can only be $F(R)R + G(R)(∂R)^2$ with $F ∼ 1/R^2$ and $G ∼ 1/R^4$, because the only scale available is the compactification radius. Translating back to the no-scale field $T$ with $T+̄T ∼ R^{α}$ and $α = √(3(k+2)/k)$ gives $ΔK ∼ 1/(T+̄T)^c$ with $c = √(3(k+2)/k)$, which for the ten-dimensional case ($k=6$) means $c=2$ and $ΔK ∼ 1/(T+̄T)^2$. If correct, this is a finite, computable, non-exponential contribution to the radion potential that is present whenever the superpotential is non-zero, and it is the leading effect for manifolds whose Euler number vanishes.

What carries the argument

The load-bearing device is the identification of the no-scale field with a power of the compactification radius, $ {Re }T = R^{α}$ with $α = √(k(k+2)/3)$, matched to the standard no-scale Kähler potential $K = -3 {ln}(T+̄T)$. This lets the authors convert a statement about the radius — that loop effects scale as $1/R^2$ in the Einstein-Hilbert term and $1/R^4$ in the kinetic term before Weyl rescaling — into a statement about the Kähler potential, $ΔK ∼ 1/(T+̄T)^c$ with $c = k + 2α = √(3(k+2)/k)$. The exponent $c$ then controls everything: the potential scales as $|W|^2 (T+̄T)^{-(c+3)}$ in the Einstein frame and $|W|^2 R^{-3α+k-2}$ in the Brans-Dicke frame, and the prefactor $c(c-1)$ vanishes exactly in the cases where no-scale structure survives.

Extended reading notes

Core claim

The paper derives the parametric form of the leading finite one-loop Kähler correction for a single no-scale volume modulus. Working in the Brans-Dicke frame, the authors observe that the one-loop terms must be shift-symmetric in $ {Im }T$ and can depend only on the radius, so they take the form $F(R)R + G(R)(∂R)^2$ with $F ∼ 1/R^2$ and $G ∼ 1/R^4$. After Weyl rescaling and rewriting in terms of $T$, this becomes a correction $ΔK ∼ 1/(T+̄T)^c$ with $c = √(3(k+2)/k)$, i.e. $c=2$ for the type IIB case with $ {Re }T ∼ R^4 ∼ V^{2/3}$. With a small constant $W$ switched on, the standard supergravity potential then yields $V ∼ |W|^2/R^8$ in the Brans-Dicke frame. The authors check the formula against the five-dimensional Scherk-Schwarz case, where it reproduces the familiar $|W|^2/R^4$ Casimir scaling, and compare with the string $α'$ correction $|W|^2/R^6$, which dominates at large volume. They note that a minimum of the combined potential sits at $R^2_{min} = 4|c_{Casimir}|/(3|c_{α'}|)$, and they argue that making this parametrically large requires small $α'$, hence strong coupling, where $S$-duality is expected to reinstate an equivalent correction. As an alternative they propose topologically complicated spaces with large Hodge numbers but small Euler number, where a large coefficient from the many light Kaluza-Klein fields could push the minimum to large volume.

Load-bearing premise

The derivation assumes the one-loop corrections are finite and depend only on the compactification radius, so that dimensional analysis alone fixes the coefficients as $1/R^2$ and $1/R^4$; the authors say explicitly that they have pretended the corrections are finite, and the numerical coefficient $c_{Casimir}$ is never computed.

Editorial extensions

If this is right

Any no-scale model with a single volume modulus acquires a finite one-loop Kähler correction with a definite exponent, so the shape of the radion potential at large volume is fixed without computing the loop integral.
For type IIB flux compactifications the correction is $|W|^2/R^8$, subleading to the $α'$ term $|W|^2/R^6$ but far larger than exponentially suppressed non-perturbative effects at large volume.
For manifolds with vanishing Euler number, where the $α'$ coefficient vanishes, the Casimir-like term becomes the leading stabilising effect.
The same formula reproduces the known $|W|^2/R^4$ Casimir potential of five-dimensional Scherk-Schwarz compactifications, providing a consistency check on the general exponent.
A combined potential with opposite-sign coefficients can produce a minimum at $R^2_{min} = 4|c_{Casimir}|/(3|c_{α'}|)$, which becomes parametrically large when the Casimir coefficient is large relative to the $α'$ coefficient.

Reading between the lines

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

If the exponent $c$ is really fixed by the radius power alone, the same bookkeeping should apply to multi-modulus Kähler sectors, where the loop correction would mix the overall volume with the other Kähler moduli and could shift the known large-volume minimum.
The proposal that large Hodge numbers with small Euler number give a large Casimir coefficient is testable in principle: a heat-kernel computation of the Kaluza-Klein spectrum on a specific orientifold would give the sign and magnitude of $c_{Casimir}$ directly.
Because the correction is a pure power of $R$, it cannot by itself produce a de Sitter uplift at large volume unless the $α'$ coefficient is tuned small; the paper's mechanism therefore leans on a numerical coincidence rather than a parametric hierarchy.
The S-duality argument that blocks a small $α'$ coefficient also suggests that any stabilisation scheme built purely on these two power-law terms should be checked in the dual frame before being trusted.

Original abstract

No-scale models arise in many compactifications of string theory and supergravity, the most prominent recent example being type IIB flux compactifications. Focussing on the case where the no-scale field is a single unstabilized volume modulus (radion), we analyse the general form of supergravity loop corrections that affect the no-scale structure of the Kaehler potential. These corrections contribute to the 4d scalar potential of the radion in a way that is similar to the Casimir effect. We discuss the interplay of this loop effect with string-theoretic alpha' corrections and its possible role in the stabilization of the radion.

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No-scale models arise in many compactifications of string theory and supergravity, the most prominent recent example being type IIB flux compactifications. Focussing on the case where the no-scale field is a single unstabilized volume modulus (radion), we analyse the general form of supergravity loop corrections that affect the no-scale structure of the Kaehler potential. These corrections contribute to the 4d scalar potential of the radion in a way that is similar to the Casimir effect. We discuss the interplay of this loop effect with string-theoretic alpha' corrections and its possible role in the stabilization of the radion.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	No-scale models arise in many compactifications of string theory and supergravity, the most prominent recent example being type IIB flux compactifications.	background 1.00	0.04	0.03	asserted 1.00
s1	Focussing on the case where the no-scale field is a single unstabilized volume modulus (radion), we analyse the general form of supergravity loop corrections that affect the no-scale structure of the Kaehler potential.	contribution 0.97	0.87	0.07	asserted 0.82
s2	These corrections contribute to the 4d scalar potential of the radion in a way that is similar to the Casimir effect.	result 0.71	0.53	0.13	asserted 1.00
s3	We discuss the interplay of this loop effect with string-theoretic alpha' corrections and its possible role in the stabilization of the radion.	contribution 0.56	0.58	0.23	hedged possibility 0.87

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References

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D7-brane position moduli in Type IIB orientifolds can serve as large-field inflatons, with a mirror-symmetry shift symmetry and flux-induced monodromy, provided the flux coefficients can be tuned small.
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...
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.
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.
On D3-brane Potentials in Compactifications with Fluxes and Wrapped D-branes
hep-th 2006-07 accept novelty 6.0 of 10

The position dependence of the volume-stabilizing nonperturbative superpotential in a warped flux compactification is given by the embedding equation of the wrapped four-cycle, raised to the power 1/N for N coincident...
On supersymmetric Minkowski vacua in IIB orientifolds
hep-th 2006-03 conditional novelty 6.0 of 10

Under an assumed racetrack superpotential, toroidal orbifold models with one or two complex structure moduli admit supersymmetric Minkowski vacua, and models without complex structure moduli can be stabilized by addin...
de Sitter String Vacua from Perturbative Kahler Corrections and Consistent D-terms
hep-th 2006-02 conditional novelty 6.0 of 10

Perturbative Kähler corrections stabilize the volume modulus while preserving the shift symmetry that a D7-brane D-term can gauge, uplifting the AdS minimum to a metastable de Sitter vacuum.
Locally stable non-supersymmetric Minkowski vacua in supergravity
hep-th 2006-02 accept novelty 6.0 of 10

In N=1 supergravity with chiral fields, a locally stable nonsupersymmetric Minkowski vacuum requires the Kähler curvature contracted with four Goldstino derivatives to stay below a fixed value, which for separable Käh...
Kahler Moduli Inflation
hep-th 2005-09 conditional novelty 6.0 of 10

A blow-up Kähler modulus in large-volume type IIB flux compactifications supplies a naturally flat inflaton direction, giving n_s = 1 - 2/N_e between 0.960 and 0.967 with a tensor fraction below 10^-10.
String Loop Corrections to Kahler Potentials in Orientifolds
hep-th 2005-08 conditional novelty 6.0 of 10

One-loop string amplitudes give explicit corrections to the Kähler potential of type IIB orientifolds that depend on both closed and open string moduli.
Moduli Stabilisation for ADD and the Dark Dimension Scenario
hep-th 2026-06 unverdicted novelty 5.0 of 10

A perturbative stabilization mechanism in the Large Volume Scenario for K3-fibered Calabi-Yau threefolds generates exponentially large 2D base volumes while keeping the 4D fibre small, enabling ADD or Dark Dimension l...
Fibre Inflation Meets Quintessence: Implications of Perturbative Stabilisation
hep-th 2025-11 reject novelty 5.0 of 10

Adding a base-modulus redefinition to fibre inflation in perturbative LVS shifts (ns, r) into ACT-allowed territory and yields an axion quintessence companion.
Warming up the Fibres
hep-th 2025-05 conditional novelty 5.0 of 10

All four fibre inflation potentials are claimed to agree with CMB observations under warm inflation, and strong dissipation can shrink the inflaton field excursion below the Planck scale.
Understanding KKLT from a 10d perspective
hep-th 2019-02 conditional novelty 5.0 of 10

The integrated trace-reversed 10d Einstein equation is equivalent to extremizing a 10d-derived 4d potential, and with a finite perfect-square gaugino action that potential still admits a KKLT uplift.
Perturbative moduli stabilisation in type IIB/F-theory framework
hep-th 2018-03 conditional novelty 5.0 of 10

All Kähler moduli of a type IIB Calabi-Yau compactification can be stabilized at a de Sitter minimum using logarithmic string-loop corrections and D-terms from magnetized D7-branes, without non-perturbative effects.
Moduli-Induced Axion Problem
hep-ph 2013-04 conditional novelty 5.0 of 10

Light moduli stabilized by SUSY breaking decay mainly into ultralight axions, and the resulting dark radiation violates Planck bounds even when the modulus is heavier than 10 TeV.
D3/D7 Branes at Singularities: Constraints from Global Embedding and Moduli Stabilisation
hep-th 2013-03 conditional novelty 5.0 of 10

A globally embedded, moduli-stabilised type IIB model with D3/D7 branes at a dP0 singularity yields TeV soft terms and, as a numerical consequence of the tuning, the observed unified gauge coupling and intermediate un...
A sufficient condition for de Sitter vacua in type IIB string theory
hep-th 2011-07 conditional novelty 5.0 of 10

A single algebraic inequality on flux and topological data is sufficient for a metastable de Sitter vacuum in type IIB Kähler-uplifted flux compactifications.
de Sitter String Vacua from Kahler Uplifting
hep-th 2006-11 conditional novelty 5.0 of 10

The leading α'^3 correction to the Kähler potential, together with gaugino condensation and flux tuning, stabilizes the volume modulus, dilaton, and complex structure moduli in a metastable de Sitter vacuum at volume ...
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.
Assisted Fibre Inflation in Perturbative LVS
hep-th 2025-06 unverdicted novelty 4.0 of 10

Multi-field fibre inflation in perturbative LVS uses collective dynamics of several moduli to achieve viable cosmology with sub-Planckian individual field ranges given by total range divided by sqrt(n).
Flux compactifications in string theory: a comprehensive review
hep-th 2005-09 accept novelty 3.0 of 10

A structured survey of type II flux compactifications: which fluxes preserve N=1, why compact spaces need orientifold planes, how fluxes generate superpotentials, and how far they go toward fixing moduli.
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...
String Cosmology: from the Early Universe to Today
hep-th 2023-03 conditional novelty 2.0 of 10

A comprehensive survey that organizes moduli stabilisation, string inflation, post-inflationary moduli domination, dark energy, and alternative early-universe scenarios into a single reference with observational targets.
String moduli inflation: an overview
hep-th 2011-08 accept novelty 2.0 of 10

Most closed-string moduli inflation models surveyed here predict negligible gravitational waves, so a Planck detection of tensor modes would rule them out.
Lectures on Naturalness, String Landscape and Multiverse
hep-th 2020-08 unverdicted novelty 1.0 of 10

Lecture notes providing a technical introduction to naturalness problems and the string theory landscape for graduate students.

How later papers used it

73 later papers cite it

Evidence: some. 62 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 4 of the 141 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 cited it as support.

Cites it as support 1 of 7 papers with this label · 1 by the same authors

By the same authors

Found that its vertices scaling the same way results in the universal form of the 1-loop correction proposed in this paper.

Loops, Local Corrections and Warping in the LVS and other Type IIB Models (2022) (same authors) · 0.96 · paraphrased: the licence does not allow quoting

How the literature uses it

73 arXiv papers cite this in 142 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 · 107 sentences without a confident label

Uses its method or tool 1 paper

Since exact string loop calculations for Calabi-Yau manifolds are not feasible, we will try to develop the parametric estimates based on dimensional analysis as suggested in [ref] .

Loops, Local Corrections and Warping in the LVS and other Type IIB Models · Naive Power Counting · 0.91

Compares with it 5 papers

This resolves a discrepancy between the field theory analysis of 1-loop corrections to the potential in [ref] on the one hand and string loop calculations by BHK [ref] and the BHP conjecture [ref] on the other hand.

Loops, Local Corrections and Warping in the LVS and other Type IIB Models · Discussion · 0.82
A similar scenario has been studied also by von Gersdorff and Hebecker [ref] .

String Loop Moduli Stabilisation and Cosmology in IIB Flux Compactifications · Survey of moduli stabilisation mechanisms · 0.86
By comparison, the recent analysis of [ref] used these conditions together with a number of conditions related to further corrections (see e.g. [ref] ) to collectively constrain the LVS.

The LVS Parametric Tadpole Constraint · Introduction · 1.00

Cites it as support 7 papers

This results in the universal form of the 1-loop correction proposed in [ref] and [ref] .

Loops, Local Corrections and Warping in the LVS and other Type IIB Models · Support by Feynman-Diagram Calculations · 0.96
Since the volume is a parameter to control the $α'$-corrections and also the string-loop corrections of order $O (V^-10/3)$ in the potential [ref] in light of the extended no-scale structure [ref] , the realization of the large volume is well-motivated to achieve a $dS$ vacuum which is meta-stable even in the presence of corrections.

Statistical Distribution of the Vacuum Energy Density in Racetrack K\"ahler Uplift Models in String Theory · Discussions · 0.98
However, the scalar potential exhibits an extended no-scale structure, and the loop corrections contribute to the scalar potential at a level subleading to their contribution to the Kähler potential and subleading to the $α'$ corrections [ref] .

General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation · Introduction · 0.97

Cites it as background 20 papers

In this scenario, one is dealing with at least three Kähler moduli and stabilisation relies, in addition to $α'$- and instanton effects, on $g_s$- or loop-corrections to the Kähler potential [ref] .

Fluxbranes: Moduli Stabilisation and Inflation · Introduction · 0.85
There are broadly two classes of string loop corrections; one follows from the prescription of [ref] where presence non-intersecting D7/O7 configurations typically leads to “KK-type" while the intersecting stacks of D7/O7 with non-contractible intersection loci lead to the so-called “Winding-type" string loop corrections.

On Global Embedding of Assisted Fibre Inflation · Introduction · 0.94
The two typical corrections known as `KK' and `winding' types are [ref]

Global Embedding of Fibre Inflation in Perturbative LVS · Fibre inflation and Kähler cone bounds on the inflaton · 0.89

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.

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