Black holes in 4d N=4 Super-Yang-Mills
Abstract
We resolve a long-standing question: does the four-dimensional N=4 SU(N) Super-Yang-Mills theory on S3 at large N contain enough states to account for the entropy of rotating electrically-charged BPS black holes in AdS5? Our answer is positive. We reconsider the large N limit of the superconformal index, using the Bethe Ansatz formulation, and find an exponentially large contribution which exactly reproduces the Bekenstein-Hawking entropy of the black holes of Gutowski-Reall. Besides, the large N limit exhibits a complicated structure, with many competing exponential contributions and Stokes lines, hinting at new physics.
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