Protected observables in supersymmetric quantum field theories (QFT’s), such as indices and BPS correlators, can often be computed exactly and non-perturbatively. These objects often admit different-looking equivalent representations, which are very helpful in the study, for instance, of strongly coupled phases of QFT’s as well as in providing new non-trivial tests of various dualities.

In this talk I will focus on 4d $mathcal{N} = 1$ gauge theories and I will present a new formula, called Bethe Ansatz type formula, which expresses the superconformal index as a sum over the solutions of a set of Bethe Ansatz equations. In describing the advantages of this new representation, I will discuss how it could be used in the framework of AdS/CFT to address the problem of black hole microstate counting.

SISSA (Trieste)