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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...

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Autores principales: Lee, Seung-Joo, Lerche, Wolfgang, Lockhart, Guglielmo, Weigand, Timo
Lenguaje:eng
Publicado: 2020
Materias:
Acceso en línea:https://dx.doi.org/10.1007/JHEP03(2022)072
http://cds.cern.ch/record/2748387
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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.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2020
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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
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AT lerchewolfgang holomorphicanomaliesfourfoldsandfluxes
AT lockhartguglielmo holomorphicanomaliesfourfoldsandfluxes
AT weigandtimo holomorphicanomaliesfourfoldsandfluxes