Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories

TL;DR

This paper investigates non-Abelian solitons in three-dimensional supersymmetric gauge theories, analyzing their zero-modes, moduli spaces, and differences between Chern-Simons and Yang-Mills formulations.

Contribution

It provides a comprehensive analysis of non-Abelian solitons, including zero-mode counting, moduli space characterization, and a comparison between Chern-Simons and Yang-Mills theories.

Findings

Zero-modes are governed by the moduli matrix H_0 for topological solitons.

Non-topological solitons' zero-modes depend on H_0 and the gauge invariant field Ω.

The master equation in YM theory is proven to be locally unique.

Abstract

We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d=2+1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological vortices of non-Abelian kinds in unbroken, broken and partially broken vacua. We calculate the number of zero-modes using an index theorem and then we apply the moduli matrix formalism to realize the moduli parameters. For the topological solitons we exhaust all the moduli while we study several examples of the non-topological and semi-local solitons. We find that the zero-modes of the topological solitons are governed by the moduli matrix H_0 only and those of the non-topological solitons are governed by both H_0 and the gauge invariant field \Omega. We prove local uniqueness of the master equation in the YM case and finally, compare all results between the CS and YM theories.