Abstract
Through the gauge-gravity duality, certain field theory quantities can provide a microscopic description of the degrees of freedom responsible for the Bekenstein-Hawking entropy of black holes. In this paper, the authors develop a powerful numerical method to study the supersymmetric index on the gauge theory side, and show how certain aspects of a class of (AdS) black holes can be extracted.
Highlights
We study the index of 4d N 1⁄4 4 Yang-Mills theory with UðNÞ gauge group, focusing on the physics of the dual Bogomolny-Prasad-Sommerfield black holes in AdS5 × S5
Has recently received some attention [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] as it successfully accounts for the thermodynamic entropy of AdS black holes
Our numerical data will nontrivially support certain recent ideas which enabled the analytic studies of these AdS black holes
Summary
Prarit Agarwal,1,* Sunjin Choi ,2,† Joonho Kim ,3,‡ Seok Kim,2,§ and June Nahmgoong 4,∥. We study the index of 4d N 1⁄4 4 Yang-Mills theory with UðNÞ gauge group, focusing on the physics of the dual Bogomolny-Prasad-Sommerfield black holes in AdS5 × S5. Certain aspects of these black holes can be studied from finite N indices with reasonably large N2. Our data clarifies and supports the recent ideas which allowed analytic studies of these black holes from the index, such as the complex saddle points of the Legendre transformation and the oscillating signs in the index. The complex saddle points naturally explain the N1-subleading oscillating patterns of the index. We illustrate the universality of our ideas by studying a model given by the inverse of the MacMahon function
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