Radiative Corrections in a Vector-Tensor Model

TL;DR

This paper investigates a vector-tensor gauge model, confirming through one-loop calculations that the tensor field has no physical degrees of freedom and analyzing its non-renormalizability when coupled with spinor fields.

Contribution

It provides a formal verification that the tensor field in the model is non-physical and explores the implications of its interactions with spinor and gravitational fields.

Findings

Tensor field contributions to vector self-energy vanish at one-loop.

Coupling tensor field with spinors leads to non-renormalizable self-energy.

Tensor field can couple to gravity but not to spinors.

Abstract

In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field.