Three-point energy correlators and the celestial block expansion

Abstract

We study the three-point energy correlator (EEEC), defined as a matrix element of a product of three energy detectors at different locations on the celestial sphere. Lorentz symmetry implies that the EEEC can be decomposed into special functions called celestial blocks. We compute three-point celestial blocks in an expansion around the collinear limit, where the three detectors approach each other on the celestial sphere. The leading term is a traditional $d{-}2$-dimensional four-point conformal block, and thus the collinear EEEC behaves like a conformally-invariant four-point function in $d{-}2$ dimensions. We obtain the coefficients of the conformal block decomposition for the collinear EEEC at leading nontrivial order in weakly-coupled $\mathcal{N}=4$ SYM and QCD. These data allow us to make certain all-orders predictions for the collinear EEEC in various kinematic limits, including the OPE limit and the double lightcone limit. We also study Ward identities satisfied by the EEEC and compute contact terms in the EEEC in weakly-coupled $\mathcal{N}=4$ SYM. Finally, we study the celestial block expansion of the EEEC in planar $\mathcal{N}=4$ SYM at strong coupling, determining celestial block coefficients to leading and first subleading order at large $\lambda$.