Vacuum Tunneling and Periodic Structure in Lattice Higgs Models

TL;DR

This paper investigates the distribution of Chern-Simons numbers in lattice Higgs models, revealing periodic structures, finite size effects, and temperature-dependent tunneling behaviors through numerical simulations.

Contribution

It introduces a geometric lattice definition of the Chern-Simons term and analyzes its effects on tunneling and distribution properties in Higgs models.

Findings

Periodic structure of Chern-Simons distributions preserved on lattice

Finite size effects explained by Haar measure

Tunneling increases at high temperature in 4d models

Abstract

Using a geometric definition for the lattice Chern-Simons term in even dimensions, we have studied the distribution of Chern-Simons numbers for the 2d-U(1) and the 4d-SU(2) lattice Higgs models. The periodic structure of the distributions is preserved in our lattice formulation and has been examined in detail. In both cases the finite size effects visible in the distribution of Chern-Simons numbers are well accounted for by the Haar measure. Moreover, we find that $\langle N_{CS}^2 \rangle$ grows with the spatial volume. We also find numerical evidence that tunneling in 4d is increased at high temperature. (PS-File including Figures available via E-mail: plache@physv.uni-bielefeld.de)