Fate of Chiral Symmetries in the Quark-Gluon Plasma from an Instanton-Based Random Matrix Model of QCD.

We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the lattice overlap Dirac operator, we propose an instanton-based random matrix model of QCD with dynamical quarks. Simulations of this model reveal that even for small quark mass the Dirac spectral density has a singularity at the origin, caused by a dilute gas of free instantons.