Fermionic fields in the d-dimensional anti-de Sitter spacetime

TL;DR

This paper investigates free massless fermionic fields with mixed symmetry in even-dimensional anti-de Sitter spacetime, deriving equations of motion, gauge transformations, and energy eigenvalues in covariant and intrinsic forms.

Contribution

It introduces a comprehensive formulation of wave equations, subsidiary conditions, and gauge transformations for mixed symmetry fermionic fields in AdS space, extending previous work to arbitrary spin and symmetry types.

Findings

Derived wave equations and subsidiary conditions for fermionic fields.

Calculated lowest energy eigenvalues for massless and gauge parameter fields.

Presented results in both covariant and intrinsic coordinate frameworks.

Abstract

Arbitrary spin free massless fermionic fields corresponding to mixed symmetry representations of the \hbox{$SO(d-1)$} compact group and propagating in even $d$-dimensional anti-de Sitter spacetime are investigated. Free wave equations of motion, subsidiary conditions and the corresponding gauge transformations for such fields are proposed. The lowest eigenvalues of the energy operator for the massless fields and the gauge parameter fields are derived. The results are formulated in $SO(d-1,2)$ covariant form as well as in terms of intrinsic coordinates.