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

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.

Automated summary

We derive an optical theorem for perturbative CFTs that computes the double discontinuity of conformal correlators by analyzing lower order correlators, similar to the optical theorem for flat space scattering amplitudes. This theorem takes a purely multiplicative form in the CFT impact parameter representation for high-energy scattering in the dual AdS theory. Through studying the four-point correlation functions dominated by graviton Regge trajectory exchange in the dual theory, we also derive constraints on one-loop vertex function for type IIB strings in AdS and general spinning tree level type IIB amplitudes in AdS.