Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices

TL;DR

This paper performs an equivariant dimensional reduction of a U(4) gauge theory over fuzzy spheres, resulting in an emergent U(1)^4 gauge theory with scalar fields, which admits vortex solutions in certain limits.

Contribution

It introduces a novel equivariant reduction of U(4) gauge theory over fuzzy spheres, leading to an emergent U(1)^4 gauge theory with vortex solutions.

Findings

Emergent U(1)^4 gauge theory with scalar fields.

Existence of vortex solutions with U(1)^3 symmetry.

Analysis of vortex properties in specific limits.

Abstract

We consider a U(4) Yang-Mills theory on M x S_F^2 x S_F^2 where M is an arbitrary Riemannian manifold and S_F^2 x S_F^2 is the product of two fuzzy spheres spontaneously generated from a SU(\cal {N}) Yang-Mills theory on M which is suitably coupled to six scalars in the adjoint of SU({\cal N}). We determine the SU(2) x SU(2)-equivariant U(4) gauge fields and perform the dimensional reduction of the theory over S_F^2 x S_F^2. The emergent model is a U(1)^4 gauge theory coupled to four complex and eight real scalar fields. We study this theory on R_2 and find that, in certain limits, it admits vortex type solutions with U(1)^3 gauge symmetry and discuss some of their properties.