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.
Highlights
In recent years it has been shown that powerful analytical results for scattering amplitudes in quantum field theory, namely the Froissart-Gribov formula and dispersion relations, have powerful CFT analogues in the Lorentzian inversion formula [1,2,3,4,5] and the two-variable CFT dispersion relation [6, 7]
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
Dispersion relations reconstruct a scattering amplitude from the discontinuity of the amplitude, while the Froissart-Gribov formula extracts the partial wave coefficients from the discontinuity and makes their analyticity in spin manifest. The utility of these methods as computational tools for scattering amplitudes stems from the fact that the discontinuity of an amplitude in perturbation theory is determined in terms of lower-loop data by the optical theorem, which in turn is a direct consequence of unitarity
Summary
In recent years it has been shown that powerful analytical results for scattering amplitudes in quantum field theory, namely the Froissart-Gribov formula and dispersion relations, have powerful CFT analogues in the Lorentzian inversion formula [1,2,3,4,5] and the two-variable CFT dispersion relation [6, 7]. The unitarity based methods to compute amplitudes inspire the development of similar unitarity methods for CFT, in particular, for the dDisc of four-point functions one gains a loop or leg order for free It was first noticed in large spin expansions [9,10,11] and later understood more generally in terms of the Lorentzian inversion formula that OPE data at oneloop can be obtained from tree-level data [12, 13]. We take finite λ (or α ) and include all tidal or stringy corrections This is made possible because the perturbative CFT optical theorem is able to describe cuts involving spinning operators, so we can take into account intermediate massive string excitations that are exchanged in the t-channel. Many technical details and additional considerations about spinning amplitudes are relegated to the appendices
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
