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

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

2012-01-03

arxiv.org/abs/1201.0728v2

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, corrected typos, added references

Scientific paper

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.

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