Sphalerons, spectral flow, and anomalies

TL;DR

This paper reviews how the topology of configuration space influences the existence of sphalerons, spectral flow, and anomalies in SU(2) Yang-Mills-Higgs theory, highlighting their interconnected roles in gauge field configurations.

Contribution

It elucidates the relationship between sphalerons, spectral flow, and anomalies, providing insights into their topological and physical interconnections in gauge theories.

Findings

Sphalerons are static, unstable solutions linked to configuration space topology.

Spectral flow of Dirac eigenvalues relates to the presence of anomalies.

The review illustrates these concepts through specific SU(2) Yang-Mills-Higgs sphalerons.

Abstract

The topology of configuration space may be responsible in part for the existence of sphalerons. Here, sphalerons are defined to be static but unstable finite-energy solutions of the classical field equations. Another manifestation of the nontrivial topology of configuration space is the phenomenon of spectral flow for the eigenvalues of the Dirac Hamiltonian. The spectral flow, in turn, is related to the possible existence of anomalies. In this review, the interconnection of these topics is illustrated for three particular sphalerons of SU(2) Yang-Mills-Higgs theory.