Thermal Fluctuations of Chern-Simons Numbers in the Lattice SU(2) Higgs Model

TL;DR

This study investigates how Chern-Simons number fluctuations in the SU(2) Higgs model vary with temperature on lattices, comparing numerical results with perturbative theories, and observing suppression of vacuum tunneling at high temperatures.

Contribution

It provides the first detailed lattice analysis of Chern-Simons number fluctuations at various temperatures in the SU(2) Higgs model, including comparisons with perturbative predictions.

Findings

Qualitative agreement with perturbative estimates.

Tendencies towards static configurations at high temperatures.

Suppression of vacuum tunneling up to about twice the Higgs transition temperature.

Abstract

We study the temperature dependence of the Chern-Simons number fluctuations in the SU(2) Higgs Model on Euclidean lattices with spatial sizes up to 20^3. Temperatures well above the Higgs phase transition $T_H$ are achieved on anisotropic lattices. Numerical results are compared to perturbative results on finite lattices as well as in continuum perturbation theory. We find qualitative agreement with perturbative estimates and see at high temperatures a tendency towards static configurations. Up to temperatures $T \simeq 2T_H$ we find indication that tunneling between vacuums with different Chern-Simons numbers are still exponentially suppressed. (Full PostScript file available via Email from plache@physw.uni-bielefeld.de )