Universality of spontaneous chiral symmetry breaking in gauge theories

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 a nonzero field. On the other hand, for a scalar mass term $m^2$ below a critical value $m_{\mathrm{c}}^2,$ 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.