Equivariant localization in supergravity in odd dimensions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914275904192512 |
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| author | Colombo, Edoardo Dimitrov, Vasil Martelli, Dario Zaffaroni, Alberto |
| author_facet | Colombo, Edoardo Dimitrov, Vasil Martelli, Dario Zaffaroni, Alberto |
| contents | We discuss a localization formula for certain integrals on odd-dimensional manifolds with boundaries, equipped with a Killing vector, and employ this to localize the regularised on-shell action of a large class of supersymmetric solutions of five dimensional minimal gauged supergravity. Specifically, we consider asymptotically AdS_5
solutions in the time-like class, in which the transverse Kähler foliation is assumed to be toric. We find that the background subtraction regularization method leads to an intriguing formula for the on-shell action, in terms of an analytic continuation of the Martelli-Sparks-Yau Sasakian volume. In particular, we show that the regularised on-shell action is
a function of the toric data of an effective compact five-dimensional manifold, as well as of the supersymmetric Killing vector, outside the corresponding dual cone. As our main example we provide a derivation of the well-known entropy function of supersymmetric and rotating black holes in AdS_5, using only topological data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant localization in supergravity in odd dimensions Colombo, Edoardo Dimitrov, Vasil Martelli, Dario Zaffaroni, Alberto High Energy Physics - Theory We discuss a localization formula for certain integrals on odd-dimensional manifolds with boundaries, equipped with a Killing vector, and employ this to localize the regularised on-shell action of a large class of supersymmetric solutions of five dimensional minimal gauged supergravity. Specifically, we consider asymptotically AdS_5 solutions in the time-like class, in which the transverse Kähler foliation is assumed to be toric. We find that the background subtraction regularization method leads to an intriguing formula for the on-shell action, in terms of an analytic continuation of the Martelli-Sparks-Yau Sasakian volume. In particular, we show that the regularised on-shell action is a function of the toric data of an effective compact five-dimensional manifold, as well as of the supersymmetric Killing vector, outside the corresponding dual cone. As our main example we provide a derivation of the well-known entropy function of supersymmetric and rotating black holes in AdS_5, using only topological data. |
| title | Equivariant localization in supergravity in odd dimensions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.15624 |