Mixed 't Hooft Anomalies and the Witten Effect for AdS Black Holes
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arXiv
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| Formato: | Preprint |
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2024
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| _version_ | 1866915274791321600 |
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| author | Heydeman, Matthew Toldo, Chiara |
| author_facet | Heydeman, Matthew Toldo, Chiara |
| contents | For a variety of BPS black holes in string theory, the supersymmetric index has provided a microscopic validation of the Bekenstein-Hawking formula. In the near-BPS limit, a gravitational path integral analysis previously revealed the semiclassical spectrum is modified, having a large extremal degeneracy (consistent with the index) and a mass gap up to a continuum of non-BPS black holes. Presently, we study examples in which these sharp features of the spectrum are altered due to the presence of anomalies in the form of $\vartheta$-angle terms in the action. These may appear generally, but we focus on near-BPS dyonic AdS$_4$ black holes in M-theory, dual to 3d $\mathcal{N}=2$ SCFTs of Class $R$ obtained by twisted compactification of $N$ wrapped M5 branes. Due to the Witten effect, the dyonic black holes receive quantum corrections to their charges, and when $\vartheta = π$ one may find a mixed `t Hooft anomaly between the $U(1)_R$ and $\mathbb{Z}_2$ time reversal symmetries. Using results from $\mathcal{N}=2$ JT supergravity, we find these effects result in a spectrum in which both the gap and index are reduced, and may even vanish. Surprisingly, for $\vartheta \rightarrow π$, neither the Bekenstein-Hawking formula nor the index correctly account for the extremal degeneracies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixed 't Hooft Anomalies and the Witten Effect for AdS Black Holes Heydeman, Matthew Toldo, Chiara High Energy Physics - Theory General Relativity and Quantum Cosmology For a variety of BPS black holes in string theory, the supersymmetric index has provided a microscopic validation of the Bekenstein-Hawking formula. In the near-BPS limit, a gravitational path integral analysis previously revealed the semiclassical spectrum is modified, having a large extremal degeneracy (consistent with the index) and a mass gap up to a continuum of non-BPS black holes. Presently, we study examples in which these sharp features of the spectrum are altered due to the presence of anomalies in the form of $\vartheta$-angle terms in the action. These may appear generally, but we focus on near-BPS dyonic AdS$_4$ black holes in M-theory, dual to 3d $\mathcal{N}=2$ SCFTs of Class $R$ obtained by twisted compactification of $N$ wrapped M5 branes. Due to the Witten effect, the dyonic black holes receive quantum corrections to their charges, and when $\vartheta = π$ one may find a mixed `t Hooft anomaly between the $U(1)_R$ and $\mathbb{Z}_2$ time reversal symmetries. Using results from $\mathcal{N}=2$ JT supergravity, we find these effects result in a spectrum in which both the gap and index are reduced, and may even vanish. Surprisingly, for $\vartheta \rightarrow π$, neither the Bekenstein-Hawking formula nor the index correctly account for the extremal degeneracies. |
| title | Mixed 't Hooft Anomalies and the Witten Effect for AdS Black Holes |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.03695 |