Note on Monopole Operators in Chern-Simons-Matter Theories

TL;DR

This paper proposes a new way to describe monopole operators directly in three-dimensional space, analyzing their properties in abelian Chern-Simons-matter theories and extending to supersymmetric cases with BPS monopoles.

Contribution

It introduces a local field behavior description of monopole operators on -space, including their dressing and spin, and extends the analysis to supersymmetric theories with BPS monopoles.

Findings

Monopole operators can be described as singular field behaviors near insertion points.

The study includes monopoles in supersymmetric theories, identifying BPS monopoles with specific properties.

Results match predictions from the superconformal index.

Abstract

Monopole operators in Chern-Simons theories with charged matter have been studied using the state-operator map in CFTs, as states on $\mathbb{R}\times S^2$ with background magnetic flux on $S^2$. Gauge invariance requires a dressing with matter modes which provides non-zero spin to the monopoles. In this note we propose a description of the monopole operators directly on $\mathbb{R}^3$, as a singular behavior of the gauge and matter fields in the vicinity of the insertion point, with a dressing. We study abelian theories with a charged boson or a charged fermion. We extend the discussion to abelian supersymmetric Chern-Simons-matter theories and describe the BPS monopoles, which have spin and preserve a single supercharge. We match our results against the prediction from the superconformal index.