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

We develop a general gauge-invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with a formulation in terms of an auxiliary Fock space, we obtain closed nonlinear symmetry algebras of higher spin fermionic fields in the AdS space and find the corresponding BRST operator. A universal procedure for constructing 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 an 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 gauge-invariant Lagrangians for massive fermionic fields of spin 1/2 and 3/2 containing the complete set of auxiliary fields and gauge symmetries.