Large p explorations. From SUGRA to big STRINGS in Mellin space

Abstract

We explore a new way of probing scattering of closed strings in AdS5×S5, which we call ‘the large p limit’. It consists of studying four-point correlators of single-particle operators in $$ \mathcal{N} $$ N = 4 SYM at large N and large ’t Hooft coupling λ, by looking at the regime in which the dual KK modes become short massive strings. In this regime the charge of the single-particle operators is order λ1/4 and the dual KK modes are in between fields and strings. Starting from SUGRA we compute the large p limit of the correlators by introducing an improved AdS5×S5 Mellin space amplitude, and we show that the correlator is dominated by a saddle point. Our results are consistent with the picture of four geodesics shooting from the boundary of AdS5×S5 towards a common bulk point, where they scatter as if they were in flat space. The Mandelstam invariants are put in correspondence with the Mellin variables and in turn with certain combinations of cross ratios. At the saddle point the dynamics of the correlator is directly related to the bulk Mellin amplitude, which in the process of taking large p becomes the flat space ten-dimensional S-matrix. We thus learn how to embed the full type IIB S-matrix in the AdS5×S5 Mellin amplitude, and how to stratify the latter in a large p expansion. We compute the large p limit of all genus zero data currently available, pointing out additional hidden simplicity of known results. We then show that the genus zero resummation at large p naturally leads to the Gross-Mende phase for the minimal area surface around the bulk point. At one-loop, we first uncover a novel and finite Mellin amplitude, and then we show that the large p limit beautifully asymptotes the gravitational S-matrix.

Towards the Virasoro-Shapiro amplitude in AdS5×S5

“…We find perfect agreement with the results from bootstrap methods of [33] (rewritten in this notation in [34]). 7…”

“…We do not here prove the existence of the effective field theory on AdS 5 ×S 5 , but justify it a posteriori by showing that it reproduces all known results for four-point correlators of single trace 1/2-BPS operators at orders in α 3 and α 5 , which were previously obtained via bootstrap methods in [29][30][31][32][33][34]. We also present a general algorithm for extending these predictions to arbitrarily high order in α and use it to obtain new predictions at α 6 and α 7 .…”

“…It presumably then makes sense to integrate a superpotential consisting of a holomorphic function of this scalar in chiral AdS×S superspace. Ultimately however we do not derive the existence of this superpotential, but justify it a posteriori by the fact that it reproduces previous results for correlators that were obtained using bootstrap methods [30][31][32][33][34]. But this does then lead to the question of the existence of an effective chiral superpotential describing the full nonlinear theory.…”

“…On the other hand, a great deal of progress has recently been achieved on the CFT side despite the CFT being strongly coupled, using the constraints imposed by superconformal and crossing symmetry as well as the simplification of the spectrum predicted by AdS/CFT (hereby summarised as 'bootstrap methods'). All tree-level single trace 1/2-BPS correlators in the supergravity limit have been obtained in this way [26][27][28] and more recently string corrections have also been bootstrapped [29][30][31][32][33][34] with groundwork laid in in [35,36]. Loop corrections to four-point AdS amplitudes have also been obtained via bootstrap methods both in the supergravity limit [37][38][39][40][41][42] as well as string corrections [30,[43][44][45].…”

“…While the approach in the above references is restricted to supergravity, ours naturally describes string corrections. However note that the results of [32][33][34] strongly hint that much of the higher dimensional conformal structure survives for the string corrections. It would therefore be interesting to investigate how these two approaches are related.…”