Lattice Chern-Simons Number Without Ultraviolet Problems

Abstract

We develop a topological method of measuring Chern-Simons number change in the real time evolution of classical lattice SU(2) and SU(2) Higgs theory. We find that the Chern-Simons number diffusion rate per physical 4-volume is very heavily suppressed in the broken phase, and that it decreases with lattice spacing in pure Yang-Mills theory, although not as quickly as predicted by Arnold, Son, and Yaffe.

Comments: 26 pages including 6 figures, uses psfig. Corrected for an algebra error in the original draft of hep-lat/9610013; minor rewriting and more analysis