Title: Unitary matrix models and random partitions: Towards universality and multi-criticality in gauge theories

Speaker: Ali Zahabi (Bourgogne)

Time: 11:30-12:05 (GMT+0), 2021.08.02

Abstract:

In this talk, I'll present some universal results in the perturbative and non-perturbative aspects of the multi-critical unitary matrix models which are obtained using the machinery of random matrices and random partitions. Precisely speaking, after a quick review on the random partitions, integrable operator formalism and their asymptotic analysis, we use (the multi-critical generalization of) the Tracy-Widom distribution and its asymptotics to explain the dynamics of the gauge theories with matrix model representation. In particular, we focus on the computation of the free energy in the weak and strong coupling regimes, which is leading to the universal multi-critical phase structure of the model. Finally, if time permits, I'll discuss the physical interpretation and explain an application of the results in a concrete example of a quiver gauge theory.