Abstract
We use tools from conformal representation theory to classify the symmetries associated to conformally soft operators in celestial CFT (CCFT) in general dimensions d. The conformal multiplets in d > 2 take the form of celestial necklaces whose structure is much richer than the celestial diamonds in d = 2, it depends on whether d is even or odd and involves mixed-symmetric tensor representations of SO(d). The existence of primary descendants in CCFT multiplets corresponds to (higher derivative) conservation equations for conformally soft operators. We lay out a unified method for constructing the conserved charges associated to operators with primary descendants. In contrast to the infinite local symmetry enhancement in CCFT2, we find the soft symmetries in CCFTd>2 to be finite-dimensional. The conserved charges that follow directly from soft theorems are trivial in d > 2, while non trivial charges associated to (generalized) currents and stress tensor are obtained from the shadow transform of soft operators which we relate to (an analytic continuation of) a specific type of primary descendants. We aim at a pedagogical discussion synthesizing various results in the literature.
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