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

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 non-perturbatively well-defined. In a finite volume, the equivariant BRST 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.