Two-loop instabilities of gauge vacua and topological symmetry breaking on R n × S 1

Abstract

The general problem of symmetry breaking by nonintegrable phase factors, or Wilson loops, on a non-simply connected spacetime of the form R n × S 1 is considered. The background field method is used to compute the effective potential as a function of a constant gauge field which solves the classical field equations. We show, in a general setting, how Wilson loops may be used to reduce this problem to a vacuum energy calculation where the fields satisfy non-trivial boundary conditions. Analysis of the one-loop effective potential is inadequate in many cases to determine stability of solutions to the effective field equations. We perform an analysis of some models where the two-loop effective potential must be used. One particular example considered is N = 4 supersymmetric Yang-Mills theory. We show that the local SU(2) symmetry in this theory breaks to U(1), but that the supersymmetry is left intact.