The Supersymmetric Index and its Holographic Interpretation

<!--HTML--><p>The supersymmetric index of N=4 SU(N) Super Yang-Mills&nbsp;is a well studied quantity. In <a href="https://arxiv.org/abs/2104.13932">2104.13932</a> we analyzed it using the Bethe Ansatz approach, expressed it as a sum and concentrated on some family of contributions to it. In the large N limit each term in this family corresponds to the contribution of a different euclidean black hole to the partition function of the dual gravitational theory. By taking into account non-perturbative contributions (wrapped D3-branes), we further showed a one to one match between the contributions of the gravitational saddles and this family of contributions to the index, both at the perturbative and non-perturbative levels. I'll end with some newer results, concerning the form of these terms at finite N, and new solutions to the Bethe Ansatz equations (i.e. additional contributions to the index beyond the ones described in that paper).</p>