Patch-wise localization with Chern-Simons forms in five dimensional supergravity
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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_ | 1866917086427611136 |
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| author | Colombo, Edoardo Dimitrov, Vasil Martelli, Dario Zaffaroni, Alberto |
| author_facet | Colombo, Edoardo Dimitrov, Vasil Martelli, Dario Zaffaroni, Alberto |
| contents | In this paper, using equivariant localization for foliations, we compute the on-shell action of a general class of supersymmetric solutions of five-dimensional gauged supergravity with vector multiplets. Unlike previous literature, we also allow for a non-trivial topology for the space-time as well as for the gauge fields. In practice, we achieve this by covering the spacetime manifold with patches and localizing in each patch. We derive a general formula for the on-shell action that depends on topological data only and can be used without a detailed knowledge of the solution. Our final result is relevant for the physically interesting examples of multi-center black holes, black rings and black lenses, topological solitons and Euclidean black saddles. We also show how to connect the topological data with the thermodynamic data: electrostatic potential, the magnetic fluxes and the possible flat connections of the solutions. Our formula for the on-shell action is derived in the context of gauged supergravity, but it is straightforward to take the ungauged limit. Thus, we reproduce known results for a large class of explicit asymptotically flat supersymmetric solutions, and we provide predictions for AdS solutions still to be found. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Patch-wise localization with Chern-Simons forms in five dimensional supergravity Colombo, Edoardo Dimitrov, Vasil Martelli, Dario Zaffaroni, Alberto High Energy Physics - Theory In this paper, using equivariant localization for foliations, we compute the on-shell action of a general class of supersymmetric solutions of five-dimensional gauged supergravity with vector multiplets. Unlike previous literature, we also allow for a non-trivial topology for the space-time as well as for the gauge fields. In practice, we achieve this by covering the spacetime manifold with patches and localizing in each patch. We derive a general formula for the on-shell action that depends on topological data only and can be used without a detailed knowledge of the solution. Our final result is relevant for the physically interesting examples of multi-center black holes, black rings and black lenses, topological solitons and Euclidean black saddles. We also show how to connect the topological data with the thermodynamic data: electrostatic potential, the magnetic fluxes and the possible flat connections of the solutions. Our formula for the on-shell action is derived in the context of gauged supergravity, but it is straightforward to take the ungauged limit. Thus, we reproduce known results for a large class of explicit asymptotically flat supersymmetric solutions, and we provide predictions for AdS solutions still to be found. |
| title | Patch-wise localization with Chern-Simons forms in five dimensional supergravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.13824 |