Radiative Corrections in Vector-Tensor Models

TL;DR

This paper investigates quantum corrections in vector-tensor field models, revealing issues with renormalizability and the effects of mass terms and couplings on degrees of freedom.

Contribution

It provides explicit one-loop calculations showing how certain couplings affect degrees of freedom and discusses the implications for renormalizability in vector-tensor theories.

Findings

Mass terms can eliminate or reintroduce degrees of freedom.

Certain couplings break renormalizability.

Stueckelberg mechanism discussed for Abelian models.

Abstract

We consider a two-form antisymmetric tensor field \phi minimally coupled to a non-abelian vector field with a field strength F. Canonical analysis suggests that a pseudoscalar mass term \frac{\mu^2}{2} \tr (\phi\wedge \phi) for the tensor field eliminates degrees of freedom associated with this field. Explicit one loop calculations show that an additional coupling m\tr(\phi\wedge F) (which can be eliminated classically by a tensor field shift) reintroduces tensor field degrees of freedom. We attribute this to the lack of the renormalizability in our vector-tensor model. We also explore a vector-tensor model with a tensor field scalar mass term \frac {\mu^2}{2} \tr (\phi\wedge\star \phi) and coupling m\tr(\phi\wedge \star F). We comment on the Stueckelberg mechanism for mass generation in the Abelian version of the latter model.