Exact flux vacua, symmetries, and the structure of the landscape

Abstract Identifying flux vacua in string theory with stabilized complex structure moduli presents a significant challenge, necessitating the minimization of a scalar potential complicated by infinitely many exponential corrections. In order to obtain exact results we connect three central topics: t...

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Main Authors: Thomas W. Grimm, Damian van de Heisteeg
Format: Article
Language:English
Published: SpringerOpen 2025-01-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP01(2025)005
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author Thomas W. Grimm
Damian van de Heisteeg
author_facet Thomas W. Grimm
Damian van de Heisteeg
author_sort Thomas W. Grimm
collection DOAJ
description Abstract Identifying flux vacua in string theory with stabilized complex structure moduli presents a significant challenge, necessitating the minimization of a scalar potential complicated by infinitely many exponential corrections. In order to obtain exact results we connect three central topics: transcendentality or algebraicity of coupling functions, emergent symmetries, and the distribution of vacua. Beginning with explicit examples, we determine the first exact landscape of flux vacua with a vanishing superpotential within F-theory compactifications on a genuine Calabi-Yau fourfold. We find that along certain symmetry loci in moduli space the generically transcendental vacuum conditions become algebraic and can be described using the periods of a K3 surface. On such loci the vacua become dense when we do not bound the flux tadpole, while imposing the tadpole bound yields a small finite landscape of distinct vacua. Away from these symmetry loci, the transcendentality of the fourfold periods ensures that there are only a finite number of vacua with a vanishing superpotential, even when the tadpole constraint is removed. These observations exemplify the general patterns emerging in the bulk of moduli space that we expose in this work. They are deeply tied to the arithmetic structure underlying flux vacua and generalize the finiteness claims about rational CFTs and rank-two attractors. From a mathematical perspective, our study is linked with the recent landmark results by Baldi, Klingler, and Ullmo about the Hodge locus that arose from connecting tame geometry and Hodge theory.
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spelling doaj-art-f022f7d4d10549e9bee9b383488b3a6b2025-01-19T12:06:49ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025119010.1007/JHEP01(2025)005Exact flux vacua, symmetries, and the structure of the landscapeThomas W. Grimm0Damian van de Heisteeg1Institute for Theoretical Physics, Utrecht UniversityCenter of Mathematical Sciences and Applications & Jefferson Physical Laboratory, Harvard UniversityAbstract Identifying flux vacua in string theory with stabilized complex structure moduli presents a significant challenge, necessitating the minimization of a scalar potential complicated by infinitely many exponential corrections. In order to obtain exact results we connect three central topics: transcendentality or algebraicity of coupling functions, emergent symmetries, and the distribution of vacua. Beginning with explicit examples, we determine the first exact landscape of flux vacua with a vanishing superpotential within F-theory compactifications on a genuine Calabi-Yau fourfold. We find that along certain symmetry loci in moduli space the generically transcendental vacuum conditions become algebraic and can be described using the periods of a K3 surface. On such loci the vacua become dense when we do not bound the flux tadpole, while imposing the tadpole bound yields a small finite landscape of distinct vacua. Away from these symmetry loci, the transcendentality of the fourfold periods ensures that there are only a finite number of vacua with a vanishing superpotential, even when the tadpole constraint is removed. These observations exemplify the general patterns emerging in the bulk of moduli space that we expose in this work. They are deeply tied to the arithmetic structure underlying flux vacua and generalize the finiteness claims about rational CFTs and rank-two attractors. From a mathematical perspective, our study is linked with the recent landmark results by Baldi, Klingler, and Ullmo about the Hodge locus that arose from connecting tame geometry and Hodge theory.https://doi.org/10.1007/JHEP01(2025)005Differential and Algebraic GeometryFlux CompactificationsSuperstring Vacua
spellingShingle Thomas W. Grimm
Damian van de Heisteeg
Exact flux vacua, symmetries, and the structure of the landscape
Journal of High Energy Physics
Differential and Algebraic Geometry
Flux Compactifications
Superstring Vacua
title Exact flux vacua, symmetries, and the structure of the landscape
title_full Exact flux vacua, symmetries, and the structure of the landscape
title_fullStr Exact flux vacua, symmetries, and the structure of the landscape
title_full_unstemmed Exact flux vacua, symmetries, and the structure of the landscape
title_short Exact flux vacua, symmetries, and the structure of the landscape
title_sort exact flux vacua symmetries and the structure of the landscape
topic Differential and Algebraic Geometry
Flux Compactifications
Superstring Vacua
url https://doi.org/10.1007/JHEP01(2025)005
work_keys_str_mv AT thomaswgrimm exactfluxvacuasymmetriesandthestructureofthelandscape
AT damianvandeheisteeg exactfluxvacuasymmetriesandthestructureofthelandscape