Shadow celestial amplitudes

Abstract

We study scattering amplitudes in the shadow conformal primary basis, which satisfies the same defining properties as the original conformal primary basis and has many advantages over it. The shadow celestial amplitudes exhibit locality manifestly on the celestial sphere, and behave like correlation functions in conformal field theory under the operator product expansion (OPE) limit. We study the OPE limits for three-point shadow celestial amplitude, and general 2 → n − 2 shadow celestial amplitudes from a certain class of Feynman diagrams. In particular, we compute the conformal block expansion of the s-channel four-point shadow celestial amplitude of massless scalars at tree-level, and show that the expansion coefficients factorize as products of OPE coefficients.

Conformal blocks from celestial gluon amplitudes

“…Before performing the block decomposition, let's firstly check the crossing symmetry for the blocks of the shadowed correlator. The 2d (14 ⇋ 23) 2 channel is obtained by switching z 2 and z 4 of G 21 34 . Now the conformal transformation is…”

“…2 . These blocks have trivial monodromy around w → e i2π w, that means the conformal blocks K 21 34 [h, h] is a single-valued combination of w and w.…”

“…However, the arguments of I u,t are 1 − w, 1/w respectively. This is a serious problem, because the arguments of Gauss hypergeometric functions should be w, w for the blocks of G 21 34 . We have met similar problems in the block decomposition of celestial gluon amplitudes [13].…”

“…Combining the blocks of I s (4.9), I t (4.16) and I u (4.17), we obtain the following conformal block decomposition of G 21 34 (w, w)…”

“…In standard CFT [7,8], the conformal block decomposition of correlation functions is the common tool to bootstrap the spectrum. Recently there has been studies on the conformal block decomposition [9][10][11][12][13][14][15][16][17][18][19][20][21] in CCFT. The detailed technique to compute the blocks in CCFT is different from that of the standard CFT.…”