AdS black holes and finite N indices

We study the index of 4d N = 4 Yang-Mills theory with U(N) gauge group, focusing on the physics of the dual Bogomolny-Prasad-Sommerfield black holes in AdS(5) x 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 <= 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 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.

Automated summary

The research focuses on the index of 4d N = 4 Yang-Mills theory with U(N) gauge group, discussing the physics of dual Bogomolny-Prasad-Sommerfield black holes in AdS(5) x S-5. Numerical studies were conducted for N <= 6, showing that the entropy of the index matches well with the Bekenstein-Hawking entropy of the dual black holes. The data clarifies recent ideas and supports the analytic studies of these black holes from the index, including complex saddle points and oscillating signs.