Instanton fermionic zero mode at finite temperature and chemical potential

TL;DR

This paper derives the fermionic zero mode solution for instantons in QCD at finite temperature and chemical potential, enabling comprehensive analysis of instanton effects across the full phase diagram.

Contribution

It provides the first explicit zero mode solution for non-zero temperature and chemical potential, expanding the understanding of instanton effects in QCD.

Findings

Derived the fermionic zero mode solution for T ≠ 0 and μ ≠ 0.

Enabled investigation of instanton density dependence on thermodynamic variables.

Facilitated studies of QCD phase diagram dynamics.

Abstract

In QCD the spontaneous breaking of chiral symmetry and the U(1) axial anomaly can be understood considering instantons as the gauge configurations mediating quark-quark interaction. The existence of an exact zero mode solution of the Dirac equation in the field of a single instanton is the fundamental ingredient of this analysis. Explicit expressions for psi_0 are available for T different from 0 and mu=0, and mu different from 0 and T=0. In this paper we derive the solution for the most general case T different from 0 and mu different from 0. This new result opens the possibility of investigating the QCD dynamics associated with instantons in the full phase diagram. As a first step in this direction we will study the dependence of the instanton density from the thermodynamic coordinates.