New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space

TL;DR

This paper uncovers new conformal-like symmetries for strictly massless higher-spin fermions in 4D de Sitter space, revealing an extended algebra that governs their gauge potentials and mode solutions.

Contribution

It introduces a novel conformal-like symmetry algebra for massless fermions in de Sitter space and analyzes its implications for gauge potentials and mode representations.

Findings

The conformal-like symmetries form an $so(4,2)$ algebra with de Sitter symmetries.

Physical modes form direct sums of Unitary Irreducible Representations of the conformal-like algebra.

The modes also constitute Discrete Series UIRs of the de Sitter algebra $so(4,1)$.

Abstract

We present new infinitesimal `conformal-like' symmetries for the field equations of strictly massless spin-$s \geq 3/2$ totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime ($dS_{4}$). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of $dS_{4}$, but they are not conventional conformal transformations. We show that the algebra generated by the ten de Sitter (dS) symmetries and the five conformal-like symmetries closes on the conformal-like algebra $so(4,2)$ up to gauge transformations of the gauge potentials. The transformations of the gauge-invariant field strength tensor-spinors under the conformal-like symmetries are given by the product of $\gamma^{5}$ times a usual infinitesimal conformal transformation of the field strengths. Furthermore, we demonstrate that the two sets of physical mode solutions, corresponding to the two helicities $\pm s$ of the strictly massless theories, form a direct sum of Unitary Irreducible Representations (UIRs) of the conformal-like algebra. We also fill a gap in the literature by explaining how these physical modes form a direct sum of Discrete Series UIRs of the dS algebra $so(4,1)$.