Topography of the hot sphaleron Transitions

TL;DR

This paper provides numerical evidence of sphaleron-like transitions in the hot electroweak phase, analyzing their topography and confirming their physical relevance through multiple simulation-based observations.

Contribution

It combines real-time simulations with eigenvalue measurements and energy lump analysis to characterize sphaleron transitions in the electroweak theory.

Findings

Evidence of sphaleron-like transitions in the symmetric phase

Change in Chern-Simons number reflects continuum physics

Detailed time-history of gauge-field fluctuations

Abstract

By numerical simulations in {\it real time} we provide evidence in favour of sphaleron like transitions in the hot, symmetric phase of the electroweak theory. Earlier performed observations of a change in the Chern-Simons number are supplemented with a measurement of the lowest eigenvalues of the three-dimensional staggered fermion Dirac operator and observations of the spatial extension of energy lumps associated with the transition. The observations corroborate on the interpretation of the change in Chern-Simons numbers as representing continuum physics, not lattice artifacts. By combining the various observations it is possible to follow in considerable detail the time-history of thermal fluctuations of the classical gauge-field configurations responsible for the change in the Chern-Simons number.