3d supersymmetric gauge theories and Hilbert series

TL;DR

This paper reviews how counting monopole operators helps compute the Hilbert series, revealing detailed structure of the chiral ring and moduli space in 3d supersymmetric gauge theories with four supercharges.

Contribution

It introduces a formula for the Hilbert series based on counting dressed 't Hooft monopole operators in 3d    gauge theories.

Findings

Provides a method to compute the Hilbert series from monopole operators.

Connects the Hilbert series to the structure of the chiral ring.

Enhances understanding of the moduli space of vacua.

Abstract

The Hilbert series is a generating function that enumerates gauge invariant chiral operators of a supersymmetric field theory with four supercharges and an R-symmetry. In this article I review how counting dressed 't Hooft monopole operators leads to a formula for the Hilbert series of a 3d $\mathcal{N}\geq 2$ gauge theory, which captures precious information about the chiral ring and the moduli space of supersymmetric vacua of the theory.