Couplings between a single massless tensor field with the mixed symmetry (3,1) and one vector field

TL;DR

This paper investigates consistent interactions between a massless tensor field with mixed symmetry (3,1) and an Abelian vector field, revealing nontrivial couplings in five dimensions that break PT invariance.

Contribution

It demonstrates the existence of nontrivial cross-couplings in five dimensions using a cohomological deformation approach within the antifield-BRST formalism.

Findings

Nontrivial cross-couplings exist in five dimensions.

Couplings break PT invariance.

Gauge transformations of the vector field are deformed.

Abstract

Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a single free massless tensor gauge field with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field have been investigated. The computations are done with the help of the deformation theory based on a cohomological approach, in the context of the antifield-BRST formalism. The main result is that there exist nontrivial cross-couplings between these types of fields in five spatiotemporal dimensions, which break the PT invariance and allow for the deformation of the gauge transformations of the vector field, but not of the gauge algebra.