Lagrangian formulation of the massless higher integer spin fields in the AdS background

TL;DR

This paper develops a Lagrangian framework for describing massless higher integer spin fields in AdS space, utilizing a nonlinear algebra of constraints and BRST quantization to ensure gauge invariance.

Contribution

It introduces a novel Lagrangian formulation for massless higher spin fields in AdS, including the construction of a nilpotent BRST charge for nonlinear constraint algebra.

Findings

Constructed the nonlinear constraint algebra for higher spin fields in AdS.

Derived the nilpotent BRST charge for the algebra.

Formulated gauge-invariant actions for arbitrary integer spin fields.

Abstract

We construct the Lagrangian description of arbitrary integer higher spin massless fields on the background of the D-dimensional anti-de Sitter space. The operator constraints in auxiliary Fock space corresponding to subsidiary conditions for irreducible unitary massless representations of the D-dimensional anti-de Sitter group are formulated. Unlike flat space, the algebra of the constraints turns out to be nonlinear and analogous to the $W_3$ algebra. We construct the nilpotent BRST charge for this nonlinear algebra and derive on its basis the correct field content and gauge invariant action describing the consistent arbitrary integer spin field dynamics in $AdS$ space.