Monopole Operators and Mirror Symmetry in Three Dimensions

TL;DR

This paper investigates monopole operators in 3d supersymmetric QEDs, confirming mirror symmetry predictions and demonstrating some operators are free fields, thus providing a proof of 3d mirror symmetry in a special case.

Contribution

It constructs monopole operators in 3d N=2 and N=4 theories using large-Nf expansion and confirms mirror symmetry predictions, establishing some operators as free fields.

Findings

Monopole operators are constructed as superconformal primaries.

Mirror symmetry predictions about monopole operators are confirmed.

Certain monopole operators in N=4 SQED with Nf=1 are shown to be free fields.

Abstract

We study vortex-creating, or monopole, operators in 3d CFTs which are the infrared limit of N=2 and N=4 supersymmetric QEDs in three dimensions. Using large-Nf expansion, we construct monopole operators which are primaries of short representations of the superconformal algebra. Mirror symmetry in three dimensions makes a number of predictions about such operators, and our results confirm these predictions. Furthermore, we argue that some of our large-Nf results are exact. This implies, in particular, that certain monopole operators in N=4 d=3 SQED with Nf=1 are free fields. This amounts to a proof of 3d mirror symmetry in a special case.