A nonabelian particle-vortex duality in gauge theories

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 $\mathcal{N}=2$ 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.

23 pages, no figures

References in corpus (5)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• On non-abelian T-dual geometries with Ramond fluxes
• Particle-vortex and Maxwell duality in the $Ad{S}_4\times {\mathbb{CP}}^3$/ABJM correspondence
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Cited by in corpus (2)

• Particle-vortex duality in topological insulators and superconductors
• Non-Abelian 3d Bosonization and Quantum Hall States