The superconformal index is a generalization of the Witten index to 4 dimensional fieid theories. It has becn 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 writtcn in diffcrent forms: as a single integrai ofiacobi thcta functions, as sums over largo N instantons or for fixed N as polynomials of elliptic intcgrals. 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.

DATA: 13-07-2016