Monopoles Can be Confined by 0, 1 or 2 Vortices

TL;DR

This paper explores the confinement of monopoles by vortices in supersymmetric gauge theories, analyzing different monopole types, their interactions, and conditions for BPS states using field theory and MQCD methods.

Contribution

It introduces a detailed classification of monopoles confined by vortices, including selection rules, vortex tensions, and BPS conditions, in theories with broken N=2 supersymmetry.

Findings

Three monopole types with different confinement mechanisms identified.

Vortex tensions are computed and conditions for BPS states established.

Selection rules for monopole-vortex interactions derived.

Abstract

There are three types of monopole in gauge theories with fundamental matter and N=2 supersymmetry broken by a superpotential. There are unconfined 0-monopoles and also 1 and 2-monopoles confined respectively by one or two vortices transforming under distinct components of the unbroken gauge group. If a Fayet-Iliopoulos term is added then there are only 2-monopoles. Monopoles transform in the bifundamental representation of two components of the unbroken gauge symmetry, and if two monopoles share a component they may form a boundstate. Selection rules for this process are found, for example vortex number is preserved modulo 2. We find the tensions of the vortices, which are in general distinct, and also the conditions under which vortices are mutually BPS. Results are derived in field theory and also in MQCD, and in quiver theories a T-dual picture may be used in which monopoles are classified by quiver diagrams with two colors of vertices.