Holomorphic anomalies, fourfolds and fluxes
Abstract 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 fou...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-03-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2022)072 |
| _version_ | 1819120923659206656 |
|---|---|
| author | Seung-Joo Lee Wolfgang Lerche Guglielmo Lockhart Timo Weigand |
| author_facet | Seung-Joo Lee Wolfgang Lerche Guglielmo Lockhart Timo Weigand |
| author_sort | Seung-Joo Lee |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-22T06:28:23Z |
| format | Article |
| id | doaj.art-38c75332a0844f60849d94e9e4eff525 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T06:28:23Z |
| publishDate | 2022-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-38c75332a0844f60849d94e9e4eff5252022-12-21T18:35:47ZengSpringerOpenJournal of High Energy Physics1029-84792022-03-012022317210.1007/JHEP03(2022)072Holomorphic anomalies, fourfolds and fluxesSeung-Joo Lee0Wolfgang Lerche1Guglielmo Lockhart2Timo Weigand3Center for Theoretical Physics of the Universe, Institute for Basic ScienceCERN, Theory DepartmentCERN, Theory DepartmentII. Institut für Theoretische Physik, Universität HamburgAbstract 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.https://doi.org/10.1007/JHEP03(2022)072F-TheoryTopological Strings |
| spellingShingle | Seung-Joo Lee Wolfgang Lerche Guglielmo Lockhart Timo Weigand Holomorphic anomalies, fourfolds and fluxes Journal of High Energy Physics F-Theory Topological Strings |
| 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 | F-Theory Topological Strings |
| url | https://doi.org/10.1007/JHEP03(2022)072 |
| work_keys_str_mv | AT seungjoolee holomorphicanomaliesfourfoldsandfluxes AT wolfganglerche holomorphicanomaliesfourfoldsandfluxes AT guglielmolockhart holomorphicanomaliesfourfoldsandfluxes AT timoweigand holomorphicanomaliesfourfoldsandfluxes |