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arXiv · 2409.01332

Localization of the 5D supergravity action and Euclidean saddles for the black hole index

Davide Cassani·Alejandro Ruipérez·Enrico Turetta
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Abstract

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.

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Davide Cassani, Alejandro Ruipérez, Enrico Turetta. 2024-10-03. Localization of the 5D supergravity action and Euclidean saddles for the black hole index. https://arxiv.org/abs/2409.01332

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