Interacting mixed-symmetry type tensor gauge fields of degrees two and three: a four-dimensional cohomological approach

TL;DR

This paper uses cohomological BRST techniques to analyze and construct an interacting model of mixed-symmetry tensor gauge fields in four dimensions, revealing a simplified deformation structure with specific interaction terms.

Contribution

It introduces a cohomological approach to construct an interacting model of mixed-symmetry tensor gauge fields with a nontrivial first-order deformation only.

Findings

Deformed gauge transformations and open gauge algebra are obtained.

The coupled Lagrangian includes a quartic vertex and mass-like terms.

First-order deformation suffices for consistent interactions.

Abstract

A special class of mixed-symmetry type tensor gauge fields of degrees two and three in four dimensions is investigated from the perspective of the Lagrangian deformation procedure based on cohomological BRST techniques. It is shown that the deformed solution to the master equation can be taken to be nonvanishing only at the first order in the coupling constant. As a consequence, we deduce an interacting model with deformed gauge transformations, an open gauge algebra and undeformed reducibility functions. The resulting coupled Lagrangian action contains a quartic vertex and some ``mass'' terms involving only the tensor of degree two. We discuss in what sense the results of the deformation procedure derived here are complementary to recent others.