Non-Chern-Simons Topological Mass Generation in (2+1) Dimensions

TL;DR

This paper introduces a novel topological field theory in (2+1) dimensions derived from a massive BF theory, demonstrating a topological mass generation mechanism and dualities with Klein-Gordon and Maxwell theories.

Contribution

It constructs new topological actions in (2+1) dimensions with mass generation and duality relations, expanding understanding beyond Chern-Simons theories.

Findings

A topological mass generation mechanism is demonstrated.

A duality between Klein-Gordon and Maxwell actions is established.

A relation between Kalb-Ramond fields and Stuckelberg theories via Buscher's duality is shown.

Abstract

By dimensional reduction of a massive BF theory, a new topological field theory is constructed in (2+1) dimensions. Two different topological terms, one involving a scalar and a Kalb-Ramond fields and another one equivalent to the four-dimensional BF term, are present. We constructed two actions with these topological terms and show that a topological mass generation mechanism can be implemented. Using the non-Chern-Simons topological term, an action is proposed leading to a classical duality relation between Klein-Gordon and Maxwell actions. We also have shown that an action in (2+1) dimensions with the Kalb-Ramond field is related by Buscher's duality transformation to a massive gauge-invariant Stuckelberg-type theory.