Classical Monopole Solutions to $\mathcal{N}=3$ Chern-Simons-Yang-Mills Theories

TL;DR

This paper constructs classical monopole solutions in $ abla=3$ Chern-Simons-Yang-Mills theories, revealing their structure and properties, and connects these solutions to supersymmetric operators in the IR superconformal field theory.

Contribution

It provides explicit monopole solutions and analyzes their properties within the $ abla=3$ Chern-Simons-Yang-Mills framework, linking them to IR superconformal operators.

Findings

Classical $rac{1}{3}$-BPS monopole solutions along RG flow.

Rich moduli space of monopole solutions.

Properties of monopole operators derived from solutions.

Abstract

We construct the component action and supersymmetry transformations of the $\mathcal{N} = 3$ Chern-Simons-Yang-Mills theory that flows in the infra red to the $\mathcal{N} = 3$ super conformal quiver Chern-Simons gauge theory obtained by Jafferis and Tomasiello in \cite{Jafferis:2008qz}. We then obtain classical $\frac{1}{3}$-BPS (and anti-BPS) solutions all along the RG flow. The solutions display a rich structure, for example, there is a non-trivial moduli space. Various properties of supersymmetric monopole operators in the infra red super conformal field theory, such as global charges and scaling dimensions can be derived from the monopole solutions we obtain in this paper; along the lines of the work of Benna, Klebanov and Klose in \cite{Benna:2009xd}.