Parity breaking at high temperature and density
  We investigate the question of parity breaking in three-dimensional Euclidean SU(2) gauge-Higgs theory by Monte Carlo simulations. We observe no sign of spontaneous parity breaking in the behaviour of both local and non-local gauge invariant operators. However, the presence of parity odd terms in the action can induce a phase transition to a parity odd ground state which is characterized by a Chern-Simons like condensate. The implications for various proposed scenarios of fermion number non-conservation is discussed. 
J. Ambj{\o}rn, K. Farakos and M. E. Shaposhnikov