AdS black holes and finite N indices

Abstract

We study the index of 4d $\mathcal{N}=4$ Yang-Mills theory with $U(N)$ gauge group, focussing on the physics of the dual BPS black holes in $Ad{S}_5\times S^5$. Certain aspects of these black holes can be studied from finite $N$ indices with reasonably large $N^2$. We make numerical studies of the index for $N\le 6$, by expanding it up to reasonably high orders in the fugacity. The entropy of the index agrees very well with the Bekenstein-Hawking entropy of the dual black holes, say at $N^2=25$ or $36$. 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. In particular, the complex saddle points naturally explain the $\frac{1}{N}$-subleading oscillating patterns of the index. We also illustrate the universality of our ideas by studying a model given by the inverse of the MacMahon function.

19 pages, 8 figures

References in corpus (6)

• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Supersymmetric multi-charge AdS_5 black holes
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• The Hilbert Series of Adjoint SQCD
• The 5d Superconformal Index at Large $N$ and Black Holes

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