Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space

TL;DR

This work provides a gauge-invariant, Lorentz-covariant formulation for massive totally symmetric fermionic fields in $(A)dS_d$ using an oscillator-based ket-vector formalism. It introduces a single mass parameter ${\rm m}$, relates it to standard conventions $m_D$ and $E_0$, and yields explicit Lagrangian operators ${\cal L}_{\rm der}$ and ${\cal M}$ together with gauge transformations, ensuring a complete, gauge-invariant description of massive fermions in $(A)dS_d$. The analysis includes the massless limit, showing a clean decomposition into a massless spin-$\left(s+\frac12\right)$ field and a massive spin-$\left(s-\frac12\right)$ field, and identifies discrete partial-masslessness points $m_{(n)}^2=-\rho\left(n+1+\frac{d-4}{2}\right)^2$ at which the field decomposes into a partial-m massless sector and a massive sector. The authors also prove the uniqueness of the Lagrangian and gauge structure under gauge-invariance and no-invariant-subspace requirements, and they confirm the $d=4$ Deser–Nilsson conjecture while generalizing to arbitrary $d>4$, with potential applications to AdS/CFT and AdS$_5\times S^5$ backgrounds.

Abstract

Massive arbitrary spin totally symmetric free fermionic fields propagating in d-dimensional (Anti)-de Sitter space-time are investigated. Gauge invariant action and the corresponding gauge transformations for such fields are proposed. The results are formulated in terms of various mass parameters used in the literature as well as the lowest eigenvalues of the energy operator. We apply our results to a study of partial masslessness of fermionic fields in (A)dS(d), and in the case of d=4 confirm the conjecture made in the earlier literature.