Instantons and chiral symmetry restoration in QCD-like theories

Abstract

At finite temperatures it is known that quark-induced interaction lead to formation of instanton-anti-instanton molecules, strongly polarized in time direction. We report first direct simulations of the statistical mechanics of the interacting instanton ensemble at finite temperatures. First of all, they confirmed that molecule formation is driving the chiral phase transition. It happens at T ⋍ 140 MeV (for two flavors) and is second order, while being weak first order if quark masses are as in QCD. We also calculated the behavior of thermodynamics, mesonic susceptibilities and screening masses near the phase transition: inside uncertaintes, all agrees with lattice results. Furthermore, the first order phase transition lines extend further in theories with larger number of flavors N f : for sufficiently small masses we have found that chiral restoration happens at T = 0 already at N f = 5.