Gauge-invariant massive BF models

TL;DR

This paper constructs consistent, gauge-invariant interactions for a BF model with scalar fields, introducing a mass term for the gauge field without relying on the Higgs mechanism, using cohomological deformation techniques.

Contribution

It presents a novel cohomological deformation method to generate gauge-invariant mass terms in BF models without spontaneous symmetry breaking.

Findings

Identifies two classes of gauge-invariant interacting theories with mass terms.

Demonstrates mass generation without Higgs mechanism.

Uses cohomological techniques for consistent interaction construction.

Abstract

Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of analyticity in the coupling constant, Lorentz covariance, spacetime locality, Poincare invariance, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure leads to two classes of gauge-invariant interacting theories with a mass term for the BF vector field $A_{\mu }$ with U(1) gauge invariance. In order to derive this result we have not used the Higgs mechanism based on spontaneous symmetry breaking.