Finite-temperature chiral transition in QCD with quarks in the fundamental and adjoint representation

TL;DR

This study investigates the nature of the finite-temperature chiral transition in QCD with fundamental and adjoint quarks, using RG analysis and perturbative series to identify conditions for continuous transitions and their universality classes.

Contribution

It provides a detailed RG analysis up to six loops to determine when the chiral transition in QCD is continuous and identifies the associated universality classes for different quark representations and flavors.

Findings

Continuous transition for N_f=2 in fundamental representation, belonging to 3D O(4) class.

Existence of a stable fixed point for U(2)_L x U(2)_R -> U(2)_V symmetry breaking.

For adjoint quarks, continuous transitions occur for N_f=1 (O(3) class) and N_f=2 (new SU(4)/SO(4) class).

Abstract

We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the fundamental and adjoint representation. Universality and renormalization-group (RG) arguments show that the possibility of having a continuous transition is related to the existence of a stable fixed point (FP) in the RG flow of a 3D Landau-Ginzburg-Wilson Phi^4 theory with the same chiral symmetry-breaking pattern. The RG flow of these theories is studied by field-theoretical approaches, computing and analyzing high-order perturbative series, up to six loops. According to this RG analysis, the transition in QCD can be continuous only for N_f=2. In this case it belongs to the 3D O(4) universality class. We also find a stable FP corresponding to a 3D universality class with symmetry breaking U(2)_L x U(2)_R -> U(2)_V, which implies that the transition can be continuous also if the axial-anomaly effects are suppressed at Tc. In the case of quarks in the adjoint representation, we can have a continuous transition for N_f=1,2. For N_f=1 it belongs to the O(3) universality class. For N_f=2 it belongs to a new 3D universality class characterized by the symmetry breaking SU(4)->SO(4).