Symmetries in Celestial CFTd

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.

Automated summary

In this study, conformal representation theory tools are used to classify the symmetries associated with conformally soft operators in celestial CFT (CCFT) in dimensions d. The celestial multiplets in d > 2 have a structure known as celestial necklaces which are much richer than the celestial diamonds in d = 2 and depend on whether d is even or odd. A unified method is presented for constructing the conserved charges associated with operators with primary descendants. Unlike CCFT2, the soft symmetries in CCFTd>2 are found to be finite-dimensional. Non-trivial charges associated with (generalized) currents and stress tensor are obtained from the shadow transform of soft operators.