Monopole operators, moduli spaces and dualities

TL;DR

This paper develops semiclassical methods to analyze BPS monopole operators in 3D N=2 superconformal theories, exploring their chiral rings, dualities, and R-charge spectra, with implications for understanding dualities and moduli spaces.

Contribution

It introduces a semiclassical quantization approach for BPS monopoles, compares chiral rings under dualities, and identifies conditions for dualities involving Chern-Simons terms.

Findings

Chiral ring structure derived from semiclassical quantization.

Dualities in 3D differ from 4D, especially with Chern-Simons terms.

Spectrum of R-charges determined via Hilbert series and volume minimization.

Abstract

We develop semiclassical methods to analyze the spectrum of BPS monopole operators for superconformal field theories in three dimensions with N=2 supersymmetry. We show that the chiral ring of the theory results from the semiclassical holomorphic quantization of the solution of classical BPS equations of motion on the cylinder. We apply this formalism to various theories. We also use these techniques to compare the chiral rings of theories that might be related to each other via Seiberg dualities in four dimensions. We find that the change of basis transformations that generate dualities in four dimensions (homological operations) generically do not work in three dimensions in the presence of Chern-Simons terms. Instead, new theories generally arise this way. When dualities are possible, the Chern-Simons couplings need to satisfy certain arithmetic congruences. We also determine the spectrum of R-charges of the chiral ring operators by assembling them on a Hilbert series and by minimizing the coefficient of the maximum pole relative to the trial R-charge. This is related to volume minimization in theories with dual supergravity setups.