Black hole microstate counting in Type IIB from 5d SCFTs

Abstract

We use recently established AdS 6 /CFT 5 dualities to count the microstates of magnetically charged AdS 6 × S 2 × Σ black holes in Type IIB. The near-horizon limit is described by solutions with AdS 2 × Σ g 1 × Σ g 2 × S 2 × Σ geometry, where Σ g i are Riemann surfaces of constant curvature and Σ is a further Riemann surface over which the geometry is warped. Our results show that the topologically twisted indices of the proposed dual superconformal field theories precisely reproduce the Bekenstein-Hawking entropy of this class of black holes. This provides further support for a prescription to compute fivedimensional topologically twisted indices put forth recently, and for the proposed dualities. We confirm the N 4 scaling found in the sphere partition functions and extend previous matches of sphere partition functions to AdS 6 solutions with monodromy. arXiv:1902.05074v2 [hep-th]

Exact results for 5d SCFTs of long quiver type

“…For K = 2 this is the rank-1 E 7 theory. The S 5 free energy was obtained numerically from localization and in supergravity in [56], and matched to very good accuracy between the two descriptions. In (2.16), the T 2K,K,2 quiver corresponds to L = 2K − 3 with N t = t + 1 for t ≤ K − 1 and N t = 2K − t − 1 for t ≥ K. The non-vanishing k t are k 1 = k K−1 = k 2K−2 = 2.…”

“…Type IIB supergravity solutions describing the near-horizon limits of 5-brane webs and 5-brane webs with 7-branes have been constructed in [34][35][36] and [37], 1 and result in large classes of explicit holographic dualities for the corresponding 5d SCFTs. Various aspects of the dualities have been studied in [43][44][45][46][47][48][49][50][51][52][53][54][55][56]. In particular, the free energy was found to scale quartically with the parameter controlling the large-N limit in supergravity [43], and this scaling was confirmed numerically using field theory methods [48,56].…”

“…The saddle point equations are solved analytically for generic quivers where all interior nodes have an effective number of flavors equal to twice the number of colors, N f = 2N , and for a sample of theories which also have N f = 2N nodes, leading to exact expressions for the squashed sphere free energies. This includes the theories for which the S 5 free energies were computed numerically in [48,56], which provided valuable intuition for the analytic computations shown here. Following [62,63], the conformal central charge characterizing the energy-momentum tensor two-point function is extracted, and we show that a universal relation between conformal central charge and S 5 free energy, found numerically for two example theories in [48], holds for all theories of the long quiver type to be discussed below.…”

Universal spinning black holes and theories of class $$ \mathcal{R} $$

“…where the lower and upper inequalities are saturated only for A , respectively, and thus dominate the saddle-point approximation. 10 Let us approach the origin from below, ω → i0 − . Then, the flat connection A (geom) N is the dominant saddle and by a standard semi-classical approximation the partition functions takes the form 11…”

“…This was first achieved for five-dimensional black holes in asymptotically flat spacetime in the seminal work [1]. For black holes in asymptotically locally AdS spacetimes this has only been recently achieved, starting with certain magnetic black holes in 4d in [2], extended in various ways in [3][4][5][6][7], for magnetic black holes in 6d in [8][9][10][11][12][13], and for spinning black holes in 5d in [14][15][16][17][18][19]. These calculations rely on holography, exploiting the properties of the asymptotic SCFT dual and the powerful supersymmetric localization techniques developed in the past decade.…”