Universal critical dynamics near the chiral phase transition and the QCD critical point

TL;DR

This paper develops a real-time functional renormalization group approach to study the dynamic universality classes of the QCD critical point and chiral phase transition, revealing their structural similarities and differences in critical behavior.

Contribution

It introduces a novel real-time FRG formulation that preserves symmetries and derives non-perturbative flow equations for Model G and H, elucidating their fixed points and critical exponents.

Findings

Identified structural similarities between Models G and H.

Derived non-perturbative RG flow equations for kinetic coefficients.

Compared fixed-point structures and critical exponents of the two models.

Abstract

We use a novel real-time formulation of the functional renormalization group (FRG) for dynamical systems with reversible mode couplings to study Model H, the conjectured dynamic universality class of the QCD critical point. We emphasize the structural similarities with Model G, conjectured to be the dynamic universality class of the chiral phase transition in the limit of two massless quark flavors. Importantly, our formulation of the real-time FRG preserves all relevant symmetries throughout the FRG flow which, e.g., guarantees the non-renormalization of the reversible mode couplings, as but one exact result. We derive non-perturbative RG flow equations for the kinetic coefficients of both, Model G and H, in parallel, and discuss commonalities and differences in the resulting fixed-point structure and dynamic critical exponents, such as weak-scaling relations which hold in either case versus the characteristic strong scaling of Model G which is absent in Model H.