Maths HEP Lunchtime Seminars: The superconformal index of N=4 SYM, exact results from a Fermi gas
12 February 2016 13:00 in CM221
The superconformal index is a generalization of the Witten index to 4 dimensional field theories. It has been known for 10 years how to count the states contributing to the index and express the result as a matrix model. I will present new results on the exact solution of this matrix model in the case of N=4 SYM. The solution can be written in different forms: as a single integral of Jacobi theta functions, as sums over large N instantons or for fixed N as polynomials of elliptic integrals. Time permitting I will explain the generalization to theories with N=2 SUSY, where for some the index can be solved completely, and for others only up to large N instantons.