The fate of chiral symmetry in the quark-gluon plasma

We propose an instanton-based random matrix model of the lowest part of the spectrum of the Dirac operator in the high temperature phase of quantum chromodynamics. Our model differs in two important ways from previously considered similar instanton models. Firstly, it is extremely simple, having only two parameters, one of which is the topological susceptibility. Secondly, it provides an excellent description of the distribution of the lowest eigenvalues of the Dirac operator, obtained from quenched lattice simulations with the overlap operator. We argue that the singular spike in the Dirac spectrum at zero is due to a gas of free instantons, and we show that for two chiral flavors, the $U(1)_A$ symmetry breaking pion minus delta susceptibility remains nonzero in the chiral limit.