Consistent interactions in a three-dimensional theory with tensor gauge fields of degrees two and three

TL;DR

This paper systematically derives all consistent interactions in a 3D tensor gauge field theory using BRST cohomology and deformation techniques, highlighting connections with Chern--Simons theory.

Contribution

It introduces a cohomological approach to classify interactions in a 3D tensor gauge field theory, extending the understanding of gauge symmetries and algebra deformations.

Findings

All consistent interactions are obtained via master equation deformation.

The local BRST cohomology guides the deformation of the action and gauge structure.

Connections between the tensor gauge theory and Chern--Simons theory are established.

Abstract

All consistent interactions in a three-dimensional theory with tensor gauge fields of degrees two and three are obtained by means of the deformation of the solution to the master equation combined with cohomological techniques. The local BRST cohomology of this model allows the deformation of the Lagrangian action, accompanying gauge symmetries and gauge algebra. The relationship with the Chern--Simons theory is discussed.