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

Vasileios A. Letsios

Vasileios A. Letsios

Nov 2023

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摘要原文

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.