Abstract
We present new infinitesimal ‘conformal-like’ symmetries for the field equations of strictly massless spin-s ≥ 3/2 totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime (dS4). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of dS4, 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(2, 4) 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 γ5 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 ±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(1, 4).
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Acknowledgments
The author is grateful to Atsushi Higuchi for useful discussions and encouragement. The author also thanks Gizem Sengör for discussions and comments, as well as Rakibur Rahman for communications. He would also like to thank Dionysios Anninos, F.F. John, Spyros Konitopoulos, Alan Rios Fukelman, Gizem Sengör, and Guillermo ‘il professore’ Silva for useful discussions and encouragement. Also, it is a pleasure to thank Xavier Bekaert and Mikhail Vasiliev for useful discussions. The author acknowledges financial support from the Department of Mathematics, University of York, and from the WW Smith Fund. Last, but not least, I would like to thank Alex for reminding me that there exist poetic qualities in life beyond poems, which was at the very least inspiring, for lack of a better wor(l)d.
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Letsios, V.A. New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space. J. High Energ. Phys. 2024, 78 (2024). https://doi.org/10.1007/JHEP05(2024)078
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DOI: https://doi.org/10.1007/JHEP05(2024)078