A nonabelian particle-vortex duality in gauge theories

TL;DR

This paper introduces a nonabelian particle-vortex duality in (2+1)-dimensional gauge theories, extending nonabelian T-duality from (1+1) dimensions, with applications to supersymmetric and vortex solutions.

Contribution

It develops a new nonabelian duality framework in (2+1) dimensions, generalizing existing abelian dualities and applying it to supersymmetric and vortex models.

Findings

Established a nonabelian particle-vortex duality in gauge theories.

Applied the duality to supersymmetric Yang-Mills and vortex models.

Demonstrated the duality's relevance to nonabelian vortex solutions.

Abstract

We define a nonabelian version of particle-vortex duality, by dimensionally extending usual (1+1)-dimensional nonabelian T-duality to (2+1) dimensions. While we will explicitly describe a global $SU(2)$ symmetry, our methods can also be applied to a larger group $G$, by gauging an appropriate subgroup. We will exemplify our duality with matter in both adjoint and fundamental representations by considering a modification of ${\cal N}=2$ supersymmetric Yang-Mills theory (Seiberg-Witten theory reduced to (2+1) dimensions), and an $SU(2)\times U(1)$ color-flavor locked theory that exhibits nonabelian vortex solutions.