Symmetries in Celestial CFT$_d$

TL;DR

This paper classifies symmetries in celestial conformal field theories across dimensions, revealing richer structures in higher dimensions and establishing methods for constructing associated conserved charges.

Contribution

It introduces a unified approach to classify symmetries and construct conserved charges in CCFT for general dimensions, highlighting differences from the 2D case.

Findings

Celestial multiplets form richer structures in higher dimensions.

Conserved charges from soft theorems are trivial in dimensions greater than two.

Non-trivial charges are related to shadow transforms and primary descendants.

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 CCFT${}_2$, we find the soft symmetries in CCFT${}_{d>2}$ 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.