Localization of the 5D supergravity action and Euclidean saddles for the black hole index
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912056327798784 |
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| author | Cassani, Davide Ruipérez, Alejandro Turetta, Enrico |
| author_facet | Cassani, Davide Ruipérez, Alejandro Turetta, Enrico |
| contents | We investigate equivariant localization of the gravitational on-shell action in odd dimensions, focusing on five-dimensional ungauged supergravity. We analyze the conditions for cancellation of boundary terms, so that the full action integral is given in terms of the odd-dimensional analog of the nuts and bolts of Gibbons-Hawking. We specialize to supersymmetric configurations with an additional ${\rm U}(1)$ symmetry preserving the supercharge and provide a formula for the localized on-shell action. We construct asymptotically flat Euclidean supersymmetric non-extremal solutions with two independent rotations and an arbitrary number of electric charges, providing black hole saddles of the gravitational path integral that computes a supersymmetric index, and evaluate their action equivariantly. We find that these Euclidean saddles interpolate between supersymmetric extremal black holes and two-center horizonless microstate geometries. The interpolation involves dialing the temperature and implementing different analytic continuations. The corresponding on-shell action does not depend on temperature but is affected by the analytic continuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localization of the 5D supergravity action and Euclidean saddles for the black hole index Cassani, Davide Ruipérez, Alejandro Turetta, Enrico High Energy Physics - Theory We investigate equivariant localization of the gravitational on-shell action in odd dimensions, focusing on five-dimensional ungauged supergravity. We analyze the conditions for cancellation of boundary terms, so that the full action integral is given in terms of the odd-dimensional analog of the nuts and bolts of Gibbons-Hawking. We specialize to supersymmetric configurations with an additional ${\rm U}(1)$ symmetry preserving the supercharge and provide a formula for the localized on-shell action. We construct asymptotically flat Euclidean supersymmetric non-extremal solutions with two independent rotations and an arbitrary number of electric charges, providing black hole saddles of the gravitational path integral that computes a supersymmetric index, and evaluate their action equivariantly. We find that these Euclidean saddles interpolate between supersymmetric extremal black holes and two-center horizonless microstate geometries. The interpolation involves dialing the temperature and implementing different analytic continuations. The corresponding on-shell action does not depend on temperature but is affected by the analytic continuations. |
| title | Localization of the 5D supergravity action and Euclidean saddles for the black hole index |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.01332 |