Black Holes in 4D N=4 Super-Yang-Mills Field Theory

By F. Benini, Paolo Milan. Physical Review X, 2018

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We resolve a long-standing question: does the four-dimensional $\mathcal{N}=4$ SU(N) Super-Yang-Mills theory on $S^3$ at large N contain enough states to account for the entropy of rotating electrically-charged BPS black holes in AdS$_5$? 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/861b2bbb474c3f05173fd62cca01beef224ba14c