The fate of chiral symmetries in the quark-gluon plasma

Author:

Tamas G. Kovacs

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th)

journal:

date:

2023-11-06 16:00:00

Abstract

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. Even though the interaction, mediated by light dynamical quarks creates small instanton-antiinstanton molecules, those do not influence the singular part of the spectrum, and this singular part is shown to dominate Banks-Casher type sums in the chiral limit. By generalizing the Banks-Casher formula for the singular spectrum, we show that in the chiral limit the chiral condensate vanishes if there are at least two massless flavors. We also resolve a long-standing debate, by demonstrating that for two massless quark flavors the $U(1)\msub{A}$ symmetry remains broken up to arbitrarily high finite temperatures.

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