Equivariant reduction of U 4 gauge theory over S F 2 S F 2 and the emergent vortices

İngilizce (OpenAlex)

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