BRST Extension of the Non-Linear Unfolded Formalism

TL;DR

This work connects BRST first-quantized quantization with Vasiliev’s non-linear unfolded formalism by constructing a BRST-extended unfolded framework. It develops a BRST parent/AKSZ viewpoint in which unfolded equations arise from a nilpotent odd vector field $Q$ on a target supermanifold and analyzes how generalized auxiliary fields and pure-gauge degrees of freedom can be added and consistently eliminated. The formalism provides a covariant, non-Lagrangian-to-Lagrangian route to encode interactions via $L_{\infty}$-algebras and AKSZ-type master actions, offering a unified language for higher-spin gauge theories and their BRST/BV quantization. It thereby clarifies how unfolded dynamics can be embedded into BRST/BV formalisms and how auxiliary constructs can be manipulated without changing physical content, with potential links to Fedosov quantization and AKSZ-BV frameworks.

Abstract

We review the construction of gauge field theories from BRST first-quantized systems and its relation to the unfolded formalism. In particular, the BRST extension of the non linear unfolded formalism is discussed in some details.