Reducing the Chern-Simons term by a symmetry

TL;DR

This paper explores how symmetry reduction of a 3D Chern-Simons term produces simpler models and impacts monopole and instanton solutions, with implications for finite-temperature theories.

Contribution

It demonstrates that symmetry reduction simplifies the Chern-Simons term into lower-dimensional models and affects the existence of monopole and instanton solutions.

Findings

Radial symmetry reduction yields a 1D quantum mechanical model.

Reduced expressions can be inserted into monopole and instanton equations.

Symmetry reduction eliminates certain monopole and instanton solutions.

Abstract

Reducing a 3-dimensional Chern-Simons term by a symmetry yields other topologically interesting structures. Specifically, reducing by radial symmetry results in a 1-dimensional quantum mechanical model, which has recently been used in an analysis of finite-temperature Chern-Simons theory. The radially symmetric expression may be inserted into 3-dimensional monopole or (2+1)-dimensional instanton equations, where it eliminates the monopole or instanton solutions.