Abstract
We discuss the string corrections to one-loop amplitudes in AdS5×S5, focussing on their expressions in Mellin space. We present the leading (α′)3 corrections to the family of correlators leftlangle {mathcal{O}}_2{mathcal{O}}_2{mathcal{O}}_p{mathcal{O}}_prightrangle at one loop and begin the exploration of the form of correlators with multiple channels. From these correlators we extract some string corrections to one- loop anomalous dimensions of families of operators of low twist.
Highlights
1 2 around the supergravity limit, N λ 0
1 2 these were given in [1, 2] and take a simple form in a Mellin representation. These results allow a resolution of the mixing of the spectrum of degenerate double trace operators which control the operator product expansion at this order, yielding a simple formula for the leading contributions to their anomalous dimensions
3 2 corrections to the one-loop amplitudes is known for the simplest correlator, that of four stress-energy multiplets, dual to four-graviton scattering in AdS5
Summary
We will consider four-point correlation functions of protected one-half BPS operators, which according to the AdS/CFT correspondence describe scattering amplitudes in AdS5×S5. The term Hp(1,0) and the order a contribution from free field theory together correspond to the contribution of tree-level supergravity. Arise from contact interaction vertices in the string theory effective action The term Hp(2,2) gives rise, in the flat space limit, to the analytic part of the one-loop string amplitude studied in [25] It is non-vanishing and it corresponds to the genus-one contribution to the modular completion of the λ−3Hp(1,6) term. In the supergravity limit and to leading order in a, the spectrum of exchanged operators is given by a set of unprotected double-trace operators with classical dimension ∆(0) = 2t +.
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