BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space

TL;DR

This paper presents a universal, gauge-invariant Lagrangian framework for fermionic higher spin fields in AdS space, utilizing BRST symmetry and auxiliary Fock space without off-shell constraints.

Contribution

It introduces a general BRST-based method for constructing gauge-invariant Lagrangians for fermionic higher spin fields in AdS space, applicable to any spin and dimension.

Findings

Derived nonlinear symmetry algebras for fermionic higher spin fields in AdS.

Constructed explicit Lagrangians for spin 1/2 and 3/2 fields.

Showed all constraints emerge from equations of motion and gauge symmetry.

Abstract

We develop a general gauge invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with formulation in terms of auxiliary Fock space we derive the closed nonlinear symmetry algebras of higher spin fermionic fields in the AdS space and find the corresponding BRST operator. A universal procedure of constructing the gauge invariant Lagrangians describing the dynamics of fermionic fields of any spin is developed. No off-shell constraints for the fields and gauge parameters are imposed from the very beginning. It is shown that all the constraints determining the irreducible representation of the AdS group arise as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive the gauge invariant Lagrangians for massive fermionic fields of spin 1/2 and 3/2 containing the total set of auxiliary fields and gauge symmetries.