FRACTIONAL STATISTICS AND THE DYNAMIC GAUGE-SYMMETRY OF YANG-MILLS-CHERN-SIMONS THEORY

We discuss the role of fractional statistics in determining the vacuum of a quantum field theory in 2 + 1 dimensions and show that the theta parameter for anyons may be determined dynamically, by the presence of a non-zero fermion condensate at finite temperature. By choosing appropriate boundary conditions, in a simplified model, the result suggests that pointlike vortices would have 3/2-pi statistics to first order in perturbation theory on the grounds of least energy. The notion of anyons with non-abelian statistics is also considered, and it is shown that the statistics gauge group can be broken by the analogue of the Hosotani mechanism, so that there may be domains of statistics around vortices as well as Yang-Mills domains. We speculate on possible observable implications of our results.