Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions

TL;DR

This paper explores how a noncommutative U(1) gauge theory derived from a higher-dimensional Yang-Mills setup admits vortex and flux-tube solutions, revealing new noncommutative solitons.

Contribution

It demonstrates the emergence of noncommutative vortices and flux-tubes from a spontaneously generated fuzzy extra dimension in Yang-Mills theories.

Findings

Existence of noncommutative vortex solutions on the Groenewald-Moyal plane.

Identification of flux-tube (fluxon) solutions in the model.

Analysis of properties of these noncommutative solitons.

Abstract

We consider a U(2) Yang-Mills theory on M x S_F^2 where M is an arbitrary noncommutative manifold and S_F^2 is a fuzzy sphere spontaneously generated from a noncommutative U(N) Yang-Mills theory on M, coupled to a triplet of scalars in the adjoint of U(N). Employing the SU(2)-equivariant gauge field constructed in arXiv:0905.2338, we perform the dimensional reduction of the theory over the fuzzy sphere. The emergent model is a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. We study this model on the Groenewald-Moyal plane and find that, in certain limits, it admits noncommutative, non-BPS vortex as well as flux-tube (fluxon) solutions and discuss some of their properties.