Noncommutative vortices and flux tubes from Yang Mills theories with spontaneously generated fuzzy extra dimensions

İngilizce (OpenAlex)

We consider a $U(2)$ Yang-Mills theory on $\mathcal{M}\ifmmode\times\else\texttimes\fi{}{S}_{F}^{2}$, where $\mathcal{M}$ is an arbitrary noncommutative manifold, and ${S}_{F}^{2}$ is a fuzzy sphere spontaneously generated from a noncommutative $U(\mathcal{N})$ Yang-Mills theory on $\mathcal{M}$, coupled to a triplet of scalars in the adjoint of $U(\mathcal{N})$. Employing the $SU(2)$-equivariant gauge field constructed in [D. Harland and S. Kurkcuoglu, Nucl. Phys. B 821, 380 (2009).], 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 $\mathcal{M}={\mathbb{R}}_{\ensuremath{\theta}}^{2}$ and find that, in certain limits, it admits noncommutative, non-Bogomol'nyi-Prasad-Somerfield vortex as well as flux-tube (fluxon) solutions and discuss some of their properties.