High Energy String Scattering in AdS

Abstract

We study the AdS Virasoro-Shapiro amplitude in the limit of fixed-angle high energy scattering. A recent representation as a world-sheet integral allows to compute the amplitude in this regime by saddle point techniques, very much as in flat space. This result is then compared to a classical scattering computation in AdS and agreement is found. As a byproduct of this comparison we show that AdS curvature corrections exponentiate in the high energy limit.

The AdS Veneziano amplitude at small curvature

“…We have three distinct consistency checks on our answer. Firstly, in the high energy limit we find that our answer takes an exponential form, as was observed for the AdS Virasoro-Shapiro amplitude in [27] and that the exponent for open strings is half of the one for closed strings, as argued in [28]. Secondly, while integrability has not yet been completed for the…”

“…In the high-energy limit of large S, T, R with S/T and S/R fixed 11 we expect the amplitude A(S, T ) to be determined by a classical computation, as shown for the closed string amplitude on AdS 5 × S 5 in [27]. We expect the form…”

“…and one can check that the closed string exponents from [17,18,27] are precisely twice as large as the ones for the open string (4.2)…”