# 5-Dimensional Black Holes, 4-Dimensional Super Yang-Mills, and 3-Dimensional Chern-Simons Theory

Presented by:
Sameer Murthy King's College London
Date:
Wednesday 26th May 2021 - 16:45 to 17:45
Venue:
INI Seminar Room 1
Session Chair:
Axel Kleinschmidt
Abstract:
The AdS/CFT correspondence predicts that the microstates of supersymmetric black holes in 5-dimensional AdS space are quantum states of the dual 4-dimensional super Yang-Mills (SYM) theory, which are captured by a certain integral over unitary matrices.
5. I will present analytical and numerical analyses of this matrix integral which show that the asymptotic growth of states at large charge agrees with that of the dual black hole microstates.
4. I will then show how a deformation of the matrix integral allows us to find large-N saddle-points and the resultant phase structure of SYM. There is an infinite family of large-N saddle points (phases) labelled by rational points, one of which is identified with the black hole. The deformation is closely related to the Bloch-Wigner elliptic dilogarithm, a function introduced by number theorists.
3. Finally, I will discuss how the (all-order!) perturbative structure of the matrix integral in each phase can be completely understood in terms of the three-dimensional effective theory obtained by dimensional reduction on a circle. This indicates that the superconformal index of four-dimensional SYM on $S^3 \times S^1$ is a master formula for the functional integrals of supersymmetric Chern-Simons theory on a family of orbifolds of $S^3$.