First order parent formulation for generic gauge field theories

TL;DR

This paper introduces a systematic way to reformulate generic gauge field theories as a first order parent system, extending the space of fields to include derivatives and form fields, facilitating both on and off-shell formulations.

Contribution

It presents a novel parent formulation for gauge theories based on BRST differential, unifying various models and connecting to AKSZ sigma models.

Findings

Reformulation of gauge theories as first order systems

Extension of field space to include derivatives and forms

Application to models like Yang-Mills, GR, and sigma models

Abstract

We show how a generic gauge field theory described by a BRST differential can systematically be reformulated as a first order parent system whose spacetime part is determined by the de Rham differential. In the spirit of Vasiliev's unfolded approach, this is done by extending the original space of fields so as to include their derivatives as new independent fields together with associated form fields. Through the inclusion of the antifield dependent part of the BRST differential, the parent formulation can be used both for on and off-shell formulations. For diffeomorphism invariant models, the parent formulation can be reformulated as an AKSZ-type sigma model. Several examples, such as the relativistic particle, parametrized theories, Yang-Mills theory, general relativity and the two dimensional sigma model are worked out in details.