Twisting and localization in supergravity: equivariant cohomology of BPS black holes
| Autor: | Jeon, Imtak, Murthy, Sameer |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP03(2019)140 |
| Popis: | We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge $Q_\text{eq}$, obeying $Q_\text{eq}^2=H$, where $H$ is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the $Q_\text{eq} \mathcal{V}$ deformation operator for the off-shell fluctuations of the Weyl multiplet around the $AdS_2 \times S^2$ saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy. Comment: V2: subsection 4.3 added, typo corrected, accepted version in JHEP; V3: typos corrected; V4: minor typos corrected |
| Databáze: | arXiv |
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