Dynamics of SU(2) lattice gauge theories

Abstract

We study the dynamics of SU(2) lattice gaugee theories by concentrating on the underlying Z 2 structures of monopoles and vortices, adding a chemical potential for monopoles. The resulting abelian nature of these objects allows us to reliable computations for a wide range of couplings. In particular, by integrating over the non-abelian SO(3) degrees of freedom at strong coupling, an effective Z 2 theory emerges which at leading order is just the dual version of the Z 2-Higgs model. The phase boundaries are predicted to a few percent, as verified by Monte Carlo simulations. Our approach provides a framework for explaining and comparing many of the recently discovered features of the theory, including the Creutz crossover and the SO(3) phase transition. Also, we speculate on the relevance of these ideas for confinement and precocious scaling.