Effective Action of Non-Abelian Monopole-Vortex Complex

TL;DR

This paper develops effective actions for non-Abelian monopole-vortex complexes in 4d N=2 supersymmetric gauge theories, revealing how monopoles and vortex moduli interact through sigma models and boundary terms.

Contribution

It constructs the effective actions for non-Abelian monopole-vortex complexes, including boundary interactions, in various gauge theories with detailed analysis.

Findings

Effective actions include 2D sigma models on vortex worldsheets.

Boundary terms describe monopole-vortex interactions.

The large mass limit simplifies the effective action to sigma models plus boundary contributions.

Abstract

We construct effective actions for non-Abelian 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) monopole-vortex complexes in 4d N = 2 supersymmetric gauge theories with gauge groups U(N), U(1) \times SO(2n) and U(1) \times USp(2n). In the color-flavor locked vacuum with degenerate hypermultiplet masses, a subgroup of the color-flavor diagonal symmetry remains unbroken and gives internal orientational moduli to vortices which confine monopoles in the Higgs phase. In this paper we discuss the effective action which describes the interactions between monopoles and the orientational moduli of non-Abelian vortices both from the bulk and vortex worldsheet theories. In the large mass limit, we find that the effective action consists of two-dimensional non-linear sigma models on vortex worldsheets and boundary terms which describes monopole-vortex interactions.