Chern-Simons term in the 4-dimensional SU(2) Higgs Model

TL;DR

This paper applies Seiberg's geometric charge to the Chern-Simons term in the 4D SU(2) Higgs model, analyzing its properties on small lattices and observing increased tunneling at high temperature.

Contribution

It introduces a method to compute the Chern-Simons term using Seiberg's geometric charge in lattice gauge theory, extending its application to the SU(2) Higgs model.

Findings

Periodic structure of the Chern-Simons density confirmed.

Tunneling increases at higher temperatures.

Method effective on small lattices near critical regions.

Abstract

Using Seiberg's definition for the geometric charge in SU(2) lattice gauge theory, we have managed to apply it also to the Chern-Simons term. We checked the periodic structure and determined the Chern-Simons density on small lattices $L^4$ and $L^3 \times 2,\, 4$ with $L=4,\, 6,\mbox{ and }8$ near the critical region in the SU(2) Higgs model. The data indicate that tunneling is increased at high temperature.