Spinning bulk-to-boundary correlators in the massless theories with Poincaré symmetry

Abstract

We classify the bulk-to-boundary correlators for general integer-spin $s$ operators in a Poincaré-invariant theory by imposing suitable fall-off conditions near future/past null infinity. Any bulk-to-boundary correlator is a linear superposition of a set of basic tensor structures fixed by the little group \text{ISO}(2) of massless particles. We map the independent tensor structures to all possible non-crossing double-line diagrams. A further mapping of the double-line diagrams to circular diagrams shows that all independent tensor structures are tensor products of loop diagrams. By extrapolating the bulk-to-boundary correlators to boundary-to-boundary correlators, we find a rich structure for general spin-$s$ operators. Furthermore, we show that the extrapolated operator lies in a type Ib spin-$s$ multiplet representation of Carrollian conformal field theory (CCFT). This is a net representation that generated by the Wigner translation generators.

62 pages