Black hole microstate counting in Type IIB from 5d SCFTs
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Springer
Received: February 28, 2019 Accepted: May 14, 2019 Published: May 22, 2019
Martin Fluder,a Seyed Morteza Hosseinia and Christoph F. Uhlemannb a
Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan b Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: We use recently established AdS6 /CFT5 dualities to count the microstates of magnetically charged AdS6 × S 2 × Σ black holes in Type IIB. The near-horizon limit is described by solutions with AdS2 × Σg1 × Σg2 × S 2 × Σ geometry, where Σgi 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 AdS6 solutions with monodromy. Keywords: AdS-CFT Correspondence, Black Holes in String Theory, Field Theories in Higher Dimensions ArXiv ePrint: 1902.05074
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)134
JHEP05(2019)134
Black hole microstate counting in Type IIB from 5d SCFTs
Contents 1 Introduction
1 3 3 6 9 11
3 Magnetic AdS6 black holes in Type IIB 3.1 AdS6 solutions in Type IIB 3.2 AdS2 × Σg1 × Σg2 × S 2 × Σ solutions 3.3 Solutions without monodromy: TN and #N,M 3.4 Partition function and black hole entropy for TN,K,j
12 12 13 14 14
4 Discussion
17
A Matrix models for the #N,M , TN and TN,K,j theories A.1 TN theories A.2 #N,M theories A.3 TN,K,j theories
19 20 21 22
B Five-sphere partition function
22
1
Introduction
The study of exactly computable quantities in supersymmetric field theories has led to dramatic progress in the non-perturbative understanding of quantum field theory. Partition functions on compact Euclidean spaces and supersymmetric indices are among the best understood examples, in particular in conjunction with AdS/CFT dualities, where they allow for rigorous tests of string theory constructions and holographic correspondences. Our focus in this work is on sphere partition functions and topologically twisted indices of five-dimensional superconformal field theories (SCFTs). The topologically twisted index [1, 2] of the ABJM theory [3] has been shown to count the microstates of magnetically charged AdS4 black holes [4] in the holographically dual gravitational theory in [5, 6]. This was soon generalized to other three- and four-dimensional gauge theories [7–18],1 as well as the five-dimensional USp(2N ) (“Seiberg”) theories which can be realized by D4-D8-O
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