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Holomorphic Anomalies, Fourfolds and Fluxes
We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic genera of N = 1 supersymmetric string theories in four dimensi...
Autores principales: | , , , |
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Lenguaje: | eng |
Publicado: |
2020
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1007/JHEP03(2022)072 http://cds.cern.ch/record/2748387 |
_version_ | 1780968974465368064 |
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author | Lee, Seung-Joo Lerche, Wolfgang Lockhart, Guglielmo Weigand, Timo |
author_facet | Lee, Seung-Joo Lerche, Wolfgang Lockhart, Guglielmo Weigand, Timo |
author_sort | Lee, Seung-Joo |
collection | CERN |
description | We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic genera of N = 1 supersymmetric string theories in four dimensions, or as generating functions for relative, genus zero Gromov-Witten invariants of fourfolds with fluxes. We derive the holomorphic anomaly equations by starting from the BCOV formalism of topological strings, and translating them into geometrical terms. The result can be recast into modular and elliptic anomaly equations. As a new feature, as compared to threefolds, we find an extra contribution which is given by a gravitational descendant invariant. This leads to linear terms in the anomaly equations, which support an algebra of derivatives mapping between partition functions of the various flux sectors. These geometric features are mirrored by certain properties of quasi-Jacobi forms. We also offer an interpretation of the physics from the viewpoint of the worldsheet theory, and comment on holomorphic anomalies at genus one. |
id | cern-2748387 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2020 |
record_format | invenio |
spelling | cern-27483872023-10-04T08:51:50Zdoi:10.1007/JHEP03(2022)072http://cds.cern.ch/record/2748387engLee, Seung-JooLerche, WolfgangLockhart, GuglielmoWeigand, TimoHolomorphic Anomalies, Fourfolds and Fluxesmath.AGMathematical Physics and Mathematicshep-thParticle Physics - TheoryWe investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic genera of N = 1 supersymmetric string theories in four dimensions, or as generating functions for relative, genus zero Gromov-Witten invariants of fourfolds with fluxes. We derive the holomorphic anomaly equations by starting from the BCOV formalism of topological strings, and translating them into geometrical terms. The result can be recast into modular and elliptic anomaly equations. As a new feature, as compared to threefolds, we find an extra contribution which is given by a gravitational descendant invariant. This leads to linear terms in the anomaly equations, which support an algebra of derivatives mapping between partition functions of the various flux sectors. These geometric features are mirrored by certain properties of quasi-Jacobi forms. We also offer an interpretation of the physics from the viewpoint of the worldsheet theory, and comment on holomorphic anomalies at genus one.We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic genera of N=1 supersymmetric string theories in four dimensions, or as generating functions for relative Gromov-Witten invariants of fourfolds with fluxes. We derive the holomorphic anomaly equations by starting from the BCOV formalism of topological strings, and translating them into geometrical terms. The result can be recast into modular and elliptic anomaly equations. As a new feature, as compared to threefolds, we find an extra contribution which is given by a gravitational descendant invariant. This leads to linear terms in the anomaly equations, which support an algebra of derivatives mapping between partition functions of the various flux sectors. These geometric features are mirrored by certain properties of quasi-Jacobi forms. We also offer an interpretation of the physics from the viewpoint of the worldsheet theory.arXiv:2012.00766oai:cds.cern.ch:27483872020-12-01 |
spellingShingle | math.AG Mathematical Physics and Mathematics hep-th Particle Physics - Theory Lee, Seung-Joo Lerche, Wolfgang Lockhart, Guglielmo Weigand, Timo Holomorphic Anomalies, Fourfolds and Fluxes |
title | Holomorphic Anomalies, Fourfolds and Fluxes |
title_full | Holomorphic Anomalies, Fourfolds and Fluxes |
title_fullStr | Holomorphic Anomalies, Fourfolds and Fluxes |
title_full_unstemmed | Holomorphic Anomalies, Fourfolds and Fluxes |
title_short | Holomorphic Anomalies, Fourfolds and Fluxes |
title_sort | holomorphic anomalies, fourfolds and fluxes |
topic | math.AG Mathematical Physics and Mathematics hep-th Particle Physics - Theory |
url | https://dx.doi.org/10.1007/JHEP03(2022)072 http://cds.cern.ch/record/2748387 |
work_keys_str_mv | AT leeseungjoo holomorphicanomaliesfourfoldsandfluxes AT lerchewolfgang holomorphicanomaliesfourfoldsandfluxes AT lockhartguglielmo holomorphicanomaliesfourfoldsandfluxes AT weigandtimo holomorphicanomaliesfourfoldsandfluxes |