Exploring Residual Gauge Symmetry Breaking

Simulations of pure-gauge SU(2) lattice gauge theory are performed in the minimal Coulomb gauge. This leaves a residual or remnant gauge symmetry still active which is global in three directions but still local in one. Using averaged fourth-dimension pointing links as a spin-like order parameter, the remnant symmetry appears to undergo spontaneous symmetry breaking at around $\beta = 2.6$. Both the Binder cumulant and the magnetization itself exhibit crossings in this region using lattices up to $20^4$, and a susceptibility peak is also observed. Finite size scaling indicates a weak first-order transition. The symmetry breaking is also observed to take place in the fundamental-adjoint plane, and is coincident with the strong first-order transition that exists there at large $\beta_{\rm{adjoint}}$. This provides confirmation that this phase transition is a symmetry-breaking transition. A well-known theorem concerning the instantaneous Coulomb potential has previously proven that a transition where such a Coulomb-gauge remnant symmetry breaks is necessarily deconfining.