Abstract
We propose a systematic procedure for obtaining all single trace 1/2-BPS correlators in mathcal{N} = 4 super Yang-Mills corresponding to the four-point tree-level amplitude for type IIB string theory in AdS5 × S5. The underlying idea is to compute generalised contact Witten diagrams coming from a 10d effective field theory on AdS5 × S5 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 mathcal{O} (α′7), and spell out a general algorithm for extending this to any order in α′.
Highlights
That the effects of quantum gravity are expected to become most important in curved backgrounds like the interior of black holes and the early Universe, it is very important to understand how to generalise the VS amplitude beyond the flat space limit
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 AdS5 × S5
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 been bootstrapped [29,30,31,32,33,34] with groundwork laid in in [35, 36]
Summary
We will describe the basic ingredients that we will use in this paper. We review 1/2-BPS correlators in N = 4 SYM, which will be the analogue of the Virasoro amplitude in AdS5×S5. We find that expanding our 10d Witten diagrams in terms of spherical coordinates gives rise to a spherical analogue of the Mellin transform and implies a generalised Mellin amplitude where AdS5 and S5 are on equal footing. We illustrate this approach by deriving a formula for all single trace 1/2-BPS four-point correlators in the supergravity approximation. The question of stringy corrections will be addressed in subsequent sections
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