Free totally (anti)symmetric massless fermionic fields in d-dimensional anti-de Sitter space

TL;DR

This paper investigates free massless fermionic fields of arbitrary spins in d-dimensional anti-de Sitter space, proposing equations of motion, gauge transformations, and analyzing their properties, including a new group-theoretic representation.

Contribution

It introduces a new formulation of equations and gauge transformations for totally (anti)symmetric massless fermionic fields in AdS space, highlighting differences between symmetric and antisymmetric cases.

Findings

Derived lowest energy values for representations

Proposed new equations of motion and gauge transformations

Discovered that antisymmetric gauge parameters are also massless fields

Abstract

Free massless fermionic fields of arbitrary spins $s>0$ corresponding to totally (anti)symmetric tensor-spinor representations of the $SO(d-1)$ compact subgroup and in $d$-dimensional anti-de Sitter space are investigated. We propose the free equations of motion, subsidiary conditions and corresponding gauge transformations for such fields. The equations obtained are used to derive the lowest energy values for the above-mentioned representations. A new representation for equations of motion and gauge transformations in terms of generators of anti-de Sitter group $SO(d-1,2)$ is found. It is demonstrated that in contrast to the symmetric case the gauge parameter of the antisymmetric massless field is also a massless field.