The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop

TL;DR

This paper derives a CFT optical theorem relating correlator discontinuities, applies it to high-energy AdS scattering dominated by graviton exchanges, and compares results with flat space string scattering to constrain string amplitudes.

Contribution

It introduces a perturbative CFT optical theorem and applies it to analyze one-loop high-energy scattering in AdS, connecting it with flat space string theory results.

Findings

Derived a multiplicative optical theorem for CFT correlators.

Analyzed one-loop graviton (Pomeron) exchange in AdS high-energy scattering.

Compared AdS correlator limits with flat space string scattering results.

Abstract

We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to describe high-energy scattering in the dual AdS theory. We use this result to study four-point correlation functions that are dominated in the Regge limit by the exchange of the graviton Regge trajectory (Pomeron) in the dual theory. At one-loop the scattering is dominated by double Pomeron exchange and receives contributions from tidal excitations of the scattering states which are efficiently described by an AdS vertex function, in close analogy with the known Regge limit result for one-loop string scattering in flat space at finite string tension. We compare the flat space limit of the conformal correlator to the flat space results and thus derive constraints on the one-loop vertex function for type IIB strings in AdS and also on general spinning tree level type IIB amplitudes in AdS.