Parent field theory and unfolding in BRST first-quantized terms

TL;DR

This paper develops a first-order parent field theory framework for BRST first-quantized gauge systems, enabling reduction to original or unfolded formulations, with applications to free higher-spin gauge theories.

Contribution

It introduces a novel construction of a parent field theory for BRST first-quantized systems that unifies original and unfolded formulations, including auxiliary field identification.

Findings

Successfully constructs a parent field theory for BRST systems.

Demonstrates reduction to original and unfolded formulations.

Applies framework to free higher-spin gauge theories.

Abstract

For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space--time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.