A minimal BV action for Vasiliev's four-dimensional higher spin gravity

TL;DR

This paper develops a minimal Batalin-Vilkovisky (BV) action for four-dimensional higher-spin gravity by reformulating Vasiliev's theory using the AKSZ method, ensuring a globally consistent gauge structure.

Contribution

It introduces a minimal BV master action for Vasiliev's higher-spin gravity, utilizing the AKSZ formalism to achieve a globally well-defined gauge-invariant framework.

Findings

Successfully reformulated Vasiliev's action into a BV master action

Achieved global consistency through boundary conditions and gauge transitions

Provided a foundation for quantization of higher-spin gravity

Abstract

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle.