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

Abstract

We present new infinitesimal `conformal-like' symmetries for the field equations of strictly massless spin-$s\ge 3/2$ totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime ($d{S}_4$). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of $d{S}_4$, 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 $so(4,1)$.

51 pages (main text is 37 pages long). This version has been accepted for publication in JHEP

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Cited by in corpus (3)

• de Sitter at all loops: the story of the Schwinger model
• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
• Unconventional conformal invariance of maximal depth partially massless fields on $d{S}_4$ and its relation to complex partially massless SUSY