GAUGE VACUA IN YANG-MILLS-CHERN-SIMONS THEORY ON TORI AND PROJECTIVE SPACES

We consider the addition of a Chern-Simons action to non-Abelian gauge theories at one-loop order. It is found that the topological mass acquired by the gauge field tends to promote the breaking of gauge symmetries on spacetimes with a toroidal compactification, provided suitable matter is present, but tends to suppress breaking on the sphere. When all matter fields are massless, there is an infinity of critical geometries for the torus which mark the line between broken and unbroken symmetry. A critical value of the curvature is found, for fixed mass, in the case of the two-sphere, but the behavior of the effective potential, with respect to the dimensionless parameter mass times radius, will be complex in general, since mass and radius have opposing effects.