Abstract
We compute the superconformal index of 3d \( \mathcal{N} \) = 2 superconformal field theories obtained from N M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence, we use perturbative invariants of SL(N, ℂ) Chern-Simons theory to determine the superconformal index in the large N limit, including corrections logarithmic in N . The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS4 black holes. We also verify that the supergravity one-loop contribution to the log N term coincides with the field theoretic result. We propose a 3d-3d formulation for the refined topologically twisted index, and provide strong evidence in support of its vanishing — which agrees with the fact that the expected dual rotating magnetically-charged black hole does not exist. This provides an interesting link between gravity and a tantalizing mathematical result.
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Benini, F., Gang, D. & Pando Zayas, L.A. Rotating black hole entropy from M5-branes. J. High Energ. Phys. 2020, 57 (2020). https://doi.org/10.1007/JHEP03(2020)057
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DOI: https://doi.org/10.1007/JHEP03(2020)057