Moduli Stabilization in Asymptotic Flux Compactifications

Grimm, Thomas W.; Plauschinn, Erik; van de Heisteeg, Damian

doi:10.48550/arxiv.2110.05511

Cited by 6 publications

(6 citation statements)

References 64 publications

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“…To test these ideas, detailed knowledge of the geometry of the degeneration and the way how it is probed by string or M-theory is required, and it is the goal of the present work to provide this information for the complex structure degenerations at infinite distance of an elliptic K3 surface. Our viewpoint takes a complementary, perhaps more geometric angle compared to the primarily Hodge theoretic approach [18][19][20][21][22][23][24][25][26][27][28][29] to infinite distance limits in the complex structure moduli space of Calabi-Yau threefolds and fourfolds. As one of the new aspects, we also analyse the role of brane moduli within the swampland conjectures of [16,17], by interpreting the complex structure deformations of the elliptic K3 surface as open string moduli of 7-branes in F-theory.…”

Section: Introductionmentioning

confidence: 99%

Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models

Lee,

Weigand

2021

Preprint

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Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3 surfaces are known to be classified according to their associated Kulikov models of Type I (finite distance), Type II or Type III (infinite distance). For elliptic K3 surfaces, we characterise the underlying Weierstrass models in detail. Similarly to the known two classes of Type II Kulikov models for elliptic K3 surfaces we find that the Weierstrass models of the more elusive Type III Kulikov models can be brought into two canonical forms. We furthermore show that all infinite distance limits are related to degenerations of Weierstrass models with non-minimal singularities in codimension one or to models with degenerating generic fibers as in the Sen limit. We explicitly work out the general structure of blowups and base changes required to remove the non-minimal singularities. These results form the basis for a classification of the infinite distance limits of elliptic K3 surfaces as probed by F-theory in the companion paper [1]. The Type III limits, in particular, are (partial) decompactification limits as signalled by an emergent affine enhancement of the symmetry algebra.Email: seungjoolee at ibs.re.kr, timo.weigand at desy.de

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Section: Introductionmentioning

confidence: 99%

Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models

Lee,

Weigand

2021

Preprint

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“…The mathematical structure of the boundaries of complex structure moduli spaces has been scrutinised from the point of view of asymptotic Hodge theory in a series of further works [32][33][34]. This program in particular has lead to important insights into the possibilities of moduli stabilisation in flux compactifications [35][36][37], a topic of central relevance in string theory. Irrespective of this progress, it is fair to say that a clear physics interpretation of the infinite towers of states, or even an identification of the parametrically leading towers, is yet to be obtained.…”

Section: Introductionmentioning

confidence: 99%

Physics of Infinite Complex Structure Limits in eight Dimensions

Lee,

Lerche,

Weigand

2021

Preprint

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We investigate infinite distance limits in the complex structure moduli space of Ftheory compactified on K3 to eight dimensions. While this is among the simplest possible arenas to test ideas about the Swampland Distance Conjecture, it is nevertheless non-trivial enough to improve our understanding of the physics for these limiting geometries, including phenomena of emergence. It also provides a perspective on infinite distance limits from the viewpoint of open strings. The paper has two quite independent themes. In the main part we show that all degenerations of elliptic K3 surfaces at infinite distance as analysed in the companion paper [1] can be interpreted as (partial) decompactification or emergent string limits in F-theory, in agreement with the Emergent String Conjecture. We present a unified geometric picture of the possible towers of states that can become light and illustrate our general claims via the connection between Kulikov models of degenerating K3 surfaces and the dual heterotic string. As an application we classify the possible maximal non-abelian Lie algebras and their Kac-Moody and loop extensions that can arise in the infinite distance limits. In the second part we discuss the infinite distance behaviour of certain exact quartic gauge couplings. We encounter a tension with the hypothesis that effective couplings should be fully generated by integrating out massive states. We show that by appropriately renormalizing the string coupling, at least partial emergence can be achieved.Email: seungjoolee at ibs.re.kr, wolfgang.lerche at cern.ch, timo.weigand at desy.de

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“…For further developments along this line, see for example[18][19][20][21][22][23][24][25][26] 3. In[32], it was found that the global Sen-limit appears rarely in a set of elliptic Calabi-Yau fourfolds that are constructed as elliptic fibrations over weak Fano threefolds.…”

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confidence: 99%

D-instanton superpotential in string theory

Kim

2022

J. High Energ. Phys.

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We study the non-perturbative superpotential generated by D(-1)-branes in type IIB compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. To compute the D-instanton superpotential, we study F-theory compactification on toric complete intersection elliptic Calabi-Yau fourfolds. We take the Sen-limit, but with finite gs, in F-theory compactifications with the restriction that all D7-branes are carrying SO(8) gauge groups, which we call the global Sen-limit. In the global Sen-limit, the axio-dilaton is not varying in the compactification manifold. We compute the Picard-Fuchs equations of elliptic Calabi-Yau fourfolds in the global Sen-limit, and show that the Picard-Fuchs equations of the elliptic fourfolds split into that of the underlying Calabi-Yau threefolds and of the elliptic fiber. We then demonstrate that this splitting property of the Picard-Fuchs equation implies that the fourform period of the elliptic Calabi-Yau fourfolds in the global Sen-limit does not contain exponentially suppressed terms $$ \mathcal{O}\left({e}^{-\pi /{g}_s}\right) $$ O e − π / g s . With this result, we finally show that in the global Sen-limit, the superpotential of the underlying type IIB compactification does not receive D(-1)-instanton contributions.

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Moduli Stabilization in Asymptotic Flux Compactifications

Cited by 6 publications

References 64 publications

Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models

Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models

Physics of Infinite Complex Structure Limits in eight Dimensions

D-instanton superpotential in string theory

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