New "metric-affine-like" generalization of Yang-Mills theory

Abstract

We suggest a new generalization of the $\mathrm{U}(n)$ Yang-Mills theory obtained by relaxing the condition of covariant constancy of the Hermitian form in the fibers, ${\nabla }_a{g}_{\alpha {\beta }^{\prime }}\ne 0$. This theory is a simpler analogue of the metric-affine gravity with ${\nabla }_a{g}_{bc}\ne 0$. In our case, connection ${\nabla }_a$ and Hermitian form $g_{\alpha {\beta }^{\prime }}$ are two independent variables so total curvature and total potential are no longer anti-Hermitian matrices: thus, along with the standard YM potential ${\mathbf{A}}_a$ and field strength tensor ${\mathbf{F}}_{ab}$, it contains non-trivially interacting fields ${\mathbf{B}}_a$, $\mathbf{h}$, and ${\mathbf{G}}_{ab}$, ${\mathbf{N}}_a$, forming a non-Abelian generalization of Stückelberg theory. Due to the spontaneous symmetry breaking $\mathrm{GL}(n,\mathbb{C})\to \mathrm{U}(n)$, these new fields can be made massive, and the limit $M\to \infty$ restores the standard YM theory.

5 pages