Renormalization of generalized vector field models in curved spacetime

We calculate the one-loop divergences for different vector field models in curved spacetime. We introduce a classification scheme based on their degeneracy structure, which encompasses the well-known models of the non-degenerate vector field, the Abelian gauge field and the Proca field. The renormalization of the generalized Proca model, which has important applications in cosmology, is more complicated. By extending standard heat-kernel techniques, we derive a closed form expression for the one-loop divergences of the generalized Proca model.