Matching 3d N=2 Vortices and Monopole Operators

TL;DR

This paper extends the analysis of monopole operators and vortices in 3d N=2 supersymmetric theories, confirming their quantum number matching for general matter content and discussing related subtleties.

Contribution

It generalizes previous monopole-vortex matching results to theories with arbitrary matter electric charges, including analysis of non-normalizable Fermi zero modes.

Findings

Quantum numbers of monopole operators match vortex states.

Verification for general matter content.

Discussion of non-normalizable Fermi zero mode effects.

Abstract

In earlier work with N. Seiberg, we explored connections between monopole operators, the Coulomb branch modulus, and vortices for 3d, N=2 supersymmetric, $U(1)_k$ Chern-Simons matter theories. We here extend the monopole / vortex matching analysis, to theories with general matter electric charges. We verify, for general matter content, that the spin and other quantum numbers of the chiral monopole operators match those of corresponding BPS vortex states, at the top and bottom of the tower associated with quantizing the vortices' Fermion zero modes. There are associated subtleties from non-normalizable Fermi zero modes, which contribute non-trivially to the BPS vortex spectrum and monopole operator matching; a proposed interpretation is further discussed here.