Consistent deformations method applied to a topological coupling of antisymmetric gauge fields in D=3

TL;DR

This paper uses the consistent deformations method to show that a specific topological coupling in three dimensions cannot be extended to a nonabelian form, limiting the generalization of certain topological models.

Contribution

It demonstrates that an abelian topological coupling between zero and two-form fields in D=3 cannot be nonabelianized, even with a connection-type one-form field.

Findings

No nonabelian generalization of the topological coupling exists.

The topologically massive model with the Kalb-Ramond field is nonextendable.

Introduction of a connection-type one form does not alter the result.

Abstract

In this work we use the method of consistent deformations of the master equation by Barnich and Henneaux in order to prove that an abelian topological coupling between a zero and a two form fields in D=3 has no nonabelian generalization. We conclude that a topologically massive model involving the Kalb-Ramond two-form field does not admit a nonabelian generalization. The introduction of a connection-type one form field keeps the previous result.