Abstract
We compute a set of structures which appear in the four-point function of protected operators of dimension two in super Yang Mills with SU(N) gauge group, at any order in a large N expansion. They are determined only by leading order CFT data. By focusing on a specific limit, we make connection with the dual supergravity amplitude in flat space, where such structures correspond to iterated s-cuts. We make several checks and we conjecture that the same interpretation holds for supergravity amplitudes on AdS5 × S5.
Highlights
Introduction and summarySince the advent of the AdS/CFT correspondence a lot of progress has been achieved in the computation of observables, in particular correlation functions of local and non local operators or equivalently scattering amplitudes of the dual string states
We compute a set of structures which appear in the four-point function of protected operators of dimension two in N = 4 super Yang Mills with SU(N ) gauge group, at any order in a large N expansion
We have found that the bulk point limit of the double discontinuity (dDisc) of the leading logarithmic term in G(κ), once logarithms are factored out, is reproduced by the iterated s-channel cut of the corresponding κ rungs ladder diagram
Summary
Since the advent of the AdS/CFT correspondence a lot of progress has been achieved in the computation of observables, in particular correlation functions of local and non local operators or equivalently scattering amplitudes of the dual string states. ’t Hooft coupling λ = g2YMN and at all loops in the large N expansion In this particular regime, often called supergravity limit, we are probing the four-point graviton amplitude in the two derivative supergravity effective action and at any genus. The first one is that at leading order in the ’t Hooft coupling λ, there are additional operators in the OPE of O2 × O2, in particular there are triple trace operators of the schematic form [Op1 Op2 Op3 ] which can potentially mix among themselves and with the double trace ones Another obstacle resides in the fact that the dDisc gets contributions from other terms in the conformal blocks expansion which cannot be expressed in terms only of tree level and one loop. To get to this relationship we study the bulk point limit and put it in relation with the
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