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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SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
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| 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. |
| format | Article |
| id | doaj-art-f022f7d4d10549e9bee9b383488b3a6b |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| 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 |