Random Matrix Theory and Quantum Chromodynamics - Recent Developments
The application of random matrix techniques in QCD and non-Abelian gauge theories in general has a long history, e.g. in counting Feynman diagrams, going back to 't Hooft and others. In this talk I will focus on a different aspect that relates the two: The low energy spectrum of the QCD Dirac operator as initiated by Shuryak and Verbaarschot. First, I will explain what is the precise approximation studied here where spectral statistics of random matrices applies, and where it can be useful in comparing to QCD lattice data. The relation is given by a particular finite volume low-energy limit, the epsilon regime of chiral perturbation theory of Gasser and Leutwyler. I will show how QCD parameters like quark masses, zero-modes, finite lattice spacing or chemical potential in the field theory can be incorporated into the random matrix ensemble. In the last part I will discuss more recent work with my former student Tim Würfel on the more heuristic inclusion of finite temperature.
This talk is mainly based on the review arXiv:1603.06011 and the paper with Tim arXiv:2110.03617 .