Mass generation for non-Abelian antisymmetric tensor fields in a three-dimensional space-time

TL;DR

This paper extends a topological model in 2+1 dimensions to a non-Abelian case, introducing a vector auxiliary field to enable mass generation for the Kalb-Ramond field, and develops a BRST quantization framework.

Contribution

It proposes a non-Abelian topological mass generation model in three dimensions using an auxiliary field, overcoming previous obstructions and establishing a BRST quantization scheme.

Findings

Achieved non-Abelian mass generation for Kalb-Ramond field in 3D

Identified the necessity of a vector auxiliary field for generalization

Developed a complete BRST and anti-BRST quantization framework

Abstract

Starting from a recently proposed Abelian topological model in (2+1) dimensions, which involve the Kalb-Ramond two form field, we study a non-Abelian generalization of the model. An obstruction for generalization is detected. However we show that the goal is achieved if we introduce a vectorial auxiliary field. Consequently, a model is proposed, exhibiting a non-Abelian topological mass generation mechanism in D=3, that provides mass for the Kalb-Ramond field. The covariant quantization of this model requires ghosts for ghosts. Therefore in order to quantize the theory we construct a complete set of BRST and anti-BRST equations using the horizontality condition.