Rotating black hole entropy from M5-branes

Abstract

We compute the superconformal index of 3d N = 2 superconformal 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 logarithmic in N corrections. The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS 4 black holes. We also verify that the supergravity one-loop contribution to the log N term coincides with the field theoretic result. We also 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, thus providing an interesting link between gravity and a tantalizing mathematical result. 3d T N [M 3 ] theoryWe start with the definition and basic properties of the 3d T N [M 3 ] theory appearing on the LHS of the 3d-3d relation (2.1). We define T N [M 3 ] := the 3d N = 2 superconformal field theory obtained from a twisted compactification of the 6d A N −1 (2,0) theory on M 3 , M 3 = a closed hyperbolic 3-manifold = H 3 /Γ .(2.2)

Universal 3d Cardy block and black hole entropy

“…• Twisted compactification of 5d, 6d SCFTs While our analysis relies on the localization computation of supersymmetric partition functions, and thus on the Lagrangian description of a theory, recently similar results are obtained for class R theories, which are generically non-Lagrangian theories, realized as twisted compactification of 6d (2,0) A N −1 theory on hyperbolic 3-manifolds [58,83,84]. The superconformal indices of those theories can be computed as topological invariants of SL(N, C) Chern-Simons theories by the 3d-3d correspondence and are shown to capture N 3 degrees of freedom of N M5-branes [48,49]. Remarkably, they satisfy the same relation (3.23):…”

Euclidean black saddles and AdS4 black holes

“…We should stress that these solutions should be different from the supersymmetric Euclidean solutions discussed in [60,61] which are relevant for the physics of supersymmetric rotating AdS 5 black holes and their relation to the superconformal index of the dual four-dimensional SCFT [77]. 19 While there is a conceptual similarity to the black saddles discussed here, the Euclidean solutions in [60,61,78,79] are constructed by analytic continuation of non-extremal JHEP10(2020)073…”

Gravitational Cardy limit and AdS black hole entropy

“…The key idea in these recent works has been to consider complex backgrounds or complex chemical potentials. This approach has now been generalized to include the microscopic counting of the entropy of rotating, electrically charged asymptotically AdS black holes in various dimensions [6][7][8][9][10][11][12][13][14]. These recent works, together with previous progress on magnetically charged asymptotically AdS black holes [15,16], provide a fairly complete and novel approach to microstate counting for asymptotically AdS black holes and mark the beginning of a new era in explorations of quantum gravity.…”