Phase with no mass gap in nonperturbatively gauge-fixed Yang-Mills theory

Abstract

An equivariantly gauge-fixed non-Abelian gauge theory is a theory in which a coset of the gauge group, not containing the maximal Abelian subgroup, is gauge fixed. Such theories are nonperturbatively well defined. In a finite volume, the equivariant Becchi-Rouet-Stora-Tyutin symmetry guarantees that expectation values of gauge-invariant operators are equal to their values in the unfixed theory. However, turning on a small breaking of this symmetry, and turning it off after the thermodynamic limit has been taken, can in principle reveal new phases. In this paper we use a combination of strong-coupling and mean-field techniques to study an $SU(2)$ Yang-Mills theory equivariantly gauge fixed to a $U(1)$ subgroup. We find evidence for the existence of a new phase in which two of the gluons becomes massive while the third one stays massless, resembling the broken phase of an $SU(2)$ theory with an adjoint Higgs field. The difference is that here this phase occurs in an asymptotically free theory.