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We propose a new way of understanding how chiral symmetry is realized in thehigh temperature phase of QCD. Based on the finding that a simple freeinstanton gas precisely describes the details of the lowest part of thespectrum of the lattice overlap Dirac operator, we propose an instanton-basedrandom matrix model of QCD with dynamical quarks. Simulations of this modelreveal that even for small quark mass the Dirac spectral density has asingularity at the origin, caused by a dilute gas of free instantons. Eventhough the interaction, mediated by light dynamical quarks creates smallinstanton-antiinstanton molecules, those do not influence the singular part ofthe spectrum, and this singular part is shown to dominate Banks-Casher typesums in the chiral limit. By generalizing the Banks-Casher formula for thesingular spectrum, we show that in the chiral limit the chiral condensatevanishes if there are at least two massless flavors. Our model also indicates apossible way of resolving a long-standing debate, as it suggests that for twomassless quark flavors the $U(1)_{A}$ symmetry is likely to remain broken up toarbitrarily high finite temperatures.

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