On a gauge-invariant deformation of a classical gauge-invariant theory

TL;DR

This paper develops a gauge-invariant deformation method for classical gauge theories using BV-formalism, enabling the derivation of non-Abelian and higher spin interactions while highlighting the potential non-locality of deformed theories.

Contribution

It introduces a systematic deformation procedure for gauge-invariant theories, explicitly constructing deformed actions and gauge generators via two arbitrary functions.

Findings

Deformation characterized by two arbitrary functions of initial fields.

Application to Abelian vector fields yields non-Abelian Yang-Mills theory.

Application to higher spin fields produces local cubic interaction vertices.

Abstract

We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.