Towards the Virasoro-Shapiro amplitude in AdS5xS5

We propose a systematic procedure for obtaining all single trace 1/2-BPS correlators in N = 4 super Yang-Mills corresponding to the four-point tree-level amplitude for type IIB string theory in AdS(5) x S-5. The underlying idea is to compute generalised contact Witten diagrams coming from a 10d effective field theory on AdS(5) x S-5 whose coefficients are fixed by the flat space Virasoro-Shapiro amplitude up to ambiguities related to commutators of the 10d covariant derivatives which require additional information such as localisation. We illustrate this procedure by computing stringy corrections to the supergravity prediction for all single trace 1/2-BPS correlators up to O(alpha ' (7)), and spell out a general algorithm for extending this to any order in alpha '.

Automated summary

A systematic procedure is proposed to obtain all single trace 1/2-BPS correlators in N=4 super Yang-Mills theory corresponding to the four-point tree-level amplitude for type IIB string theory in AdS(5) x S-5. This involves computing generalised contact Witten diagrams from a 10-dimensional effective field theory on AdS(5) x S-5 whose coefficients are determined by the flat space Virasoro-Shapiro amplitude, with ambiguities related to commutators of 10-dimensional covariant derivatives that require additional information like localisation. Stringy corrections to the supergravity prediction for all single trace 1/2-BPS correlators up to O(alpha' (7)) are computed as an illustration of this procedure, along with a general algorithm for extending it to any order in alpha'.