Medium induced mixing, spatial modulations and critical modes in QCD

TL;DR

This paper explores the extensive mixing of chiral condensate, density, and gluonic degrees of freedom in hot and dense QCD, revealing complex eigenvalues and spatially modulated correlations near critical points.

Contribution

It uncovers the non-Hermitian nature of the QCD effective action Hessian and the complex structure of critical modes involving multiple degrees of freedom.

Findings

Hessian of QCD effective action is non-Hermitian with symmetry under charge and complex conjugation.

Eigenvalues can form complex-conjugate pairs, indicating spatially modulated correlations.

Critical modes involve chiral condensate, density, and Polyakov loops, and are disconnected from the vacuum condensate due to avoided crossing.

Abstract

The mixing between the chiral condensate and the density in hot and dense QCD matter is familiar. We show that the mixing relevant for the ground state is considerably more extensive, and in particular also involves gluonic degrees of freedom. As a result, the Hessian of the QCD effective action is non-Hermitian, but retains a symmetry under combined charge- and complex conjugation. This can lead to complex-conjugate pairs of eigenvalues of this Hessian, signaling regimes with spatially modulated correlations. Furthermore, based on the analytic structure of the quark determinant at a chiral critical point, we demonstrate that the corresponding massless critical mode is composed of the chiral condensate, the density and the Polyakov loops. Due to an avoided crossing, the critical mode turns out to be disconnected from the chiral condensate in vacuum. We present general arguments for all these features and illustrate them through explicit model calculations.