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Unconventional conformal invariance of maximal depth partially massless fields on $dS_{4}$ and its relation to complex partially massless SUSY

Vasileios A. Letsios
Nov 2023
We present, for the first time, covariant expressions for the infinitesimal conformal symmetry transformations for maximal depth partially massless fields of spin-$s \geq 2$ on four-dimensional de Sitter spacetime ($dS_{4}$). In the spin-2 case, the invariance of both the field equations and the covariant action is demonstrated. For spin-$s >2$, the invariance is demonstrated only at the level of the field equations. For all spins $s \geq 2$, we show that the algebra does not close on the conformal algebra, $so(4,2)$, (in agreement with previous statements in the literature) due to the appearance of new symmetry transformations that contain higher derivatives. We thus call our conformal transformations `unconventional'. Our results concerning the closure of the full symmetry algebra are inconclusive. Then we shift focus to the question of supersymmetry (SUSY) on $dS_{4}$ and our objective is twofold. First, we uncover a non-interacting supermultiplet that consists of a complex partially massless spin-2 field and a complex spin-3/2 field with zero mass parameter on $dS_{4}$. Second, we showcase the appearance of the unconventional conformal symmetries in the bosonic subalgebra of our supermultiplet (the bosonic subalgebra is neither $so(4,1)$ nor $so(4,2)$, while its full structure is currently unknown). Open questions arising from our findings are also discussed.
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