Universality of spontaneous chiral symmetry breaking in gauge theories

TL;DR

This paper demonstrates that gauge theories with a scalar field exhibit a universal behavior in chiral symmetry breaking, connecting different universality classes through renormalization group flows.

Contribution

It reveals the conditions under which scalar fields become unobservable in gauge theories and connects chiral symmetry breaking mechanisms via renormalization group analysis.

Findings

Universality class includes QCD with scalar fields at large coupling.

Scalar effects become unobservable in the QCD universality class.

Spontaneous chiral symmetry breaking occurs below a critical scalar mass.

Abstract

We investigate one-flavor QCD with an additional chiral scalar field. For a large domain in the space of coupling constants, this model belongs to the same universality class as QCD, and the effects of the scalar become unobservable. This is connected to a ``bound-state fixed point'' of the renormalization flow for which all memory of the microscopic scalar interactions is lost. The QCD domain includes a microscopic scalar potential with minima at nonzero field. On the other hand, for a scalar mass term m^2 below a critical value m_c^2, the universality class is characterized by perturbative spontaneous chiral symmetry breaking which renders the quarks massive. Our renormalization group analysis shows how this universality class is continuously connected with the QCD universality class.