Off-shell Gauge Fields from BRST Quantization

Abstract

We propose a construction for nonlinear off-shell gauge field theories based on a constrained system quantized in the sense of deformation quantization. The key idea is to consider the star-product BFV--BRST master equation as an equation of motion. The construction is formulated in terms of the BRST extention of the unfolded formalism that can also be understood as an appropriate generalization of the AKSZ procedure. As an application, we consider a very simple constrained system, a quantized scalar particle, and show that it gives rise to an off-shell higher-spin gauge theory that automatically appears in the parent form and properly takes the familiar trace constraint into account. In particular, we derive a geometrically transparent form of the off-shell higher-spin theory on the AdS background.