Eikonal approximation in celestial CFT

Abstract

We identify an eikonal regime in celestial CFT2 in which massless 2-2 scattering is dominated by t-channel exchange. We derive a formula for the celestial amplitude that resums exchanges of arbitrary integer spin to all orders in the coupling. The resulting eikonal phase takes the same form as in flat space with the powers of center-of-mass energy replaced by weight-shifting operators on the celestial sphere. We independently compute the celestial two-point function for a scalar propagating in a shockwave background and show that to leading order in the gravitational coupling and for a suitable choice of the source, the result agrees with the prediction from the celestial eikonal formula for graviton exchange. We demonstrate that this two-point function can be directly obtained from the corresponding formula in AdS4 in a flat space limit. We finally establish a general relation between scalar celestial amplitudes in celestial CFTd−1 and the flat space limit of scalar AdSd+1 Witten diagrams.