Chiral symmetry restoration in QC_2D from effective model using the functional renormalization group

TL;DR

This paper investigates the nature of the chiral phase transition in two-color, two-flavor QC$_2$D using the functional renormalization group, revealing complex fixed-point structures and conditions for second-order transitions.

Contribution

It introduces a detailed FRG analysis of the fixed-point structure in QC$_2$D, comparing it with perturbative approaches and highlighting the role of axial anomalies in phase transition order.

Findings

Infrared stable $O(6)$ fixed point at infinite axial anomaly

Existence of $U_A(1)$ anomaly-free fixed points that can become stable

Phase transition can be second order, depending on anomaly behavior

Abstract

The order of the chiral phase transition in two-color and two-flavor QC$_2$D is investigated using the functional renormalization group (FRG) technique in an effective model setting. We calculate the $\beta$ function of all couplings in the dimensionally reduced Ginzburg-Landau free energy functional with Pauli-G\"ursey SU(4) symmetry. We compare results of the perturbative $\epsilon$ expansion approach with those obtained via the FRG, evaluated directly in $d=3$ dimensions. The perturbative results suggest that the fixed-point structure is more intricate than that of three-color QCD, a conclusion further supported by the FRG analysis. Both methods display an infrared stable $O(6)$ fixed point at infinite axial anomaly; however, the FRG approach also reveals the existence of $U_A(1)$ anomaly-free fixed points, which can become infrared stable if the anomaly in the underlying theory vanishes at the critical temperature. These findings imply that the phase transition can be of second order, consistent with earlier findings for three colors.