Towards all loop supergravity amplitudes on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>AdS</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>5</mml:mn></mml:msup></mml:math>

Abstract

We study the four-point function of the superconformal primary of the stress-tensor multiplet in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory, at strong coupling and in a large-$N$ expansion. This observable is holographically dual to a four-graviton amplitude in type IIB supergravity on ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$. We construct the maximal transcendental weight piece of the correlator at order ${N}^{\ensuremath{-}6}$ and compare it with the flat-space limit of the corresponding two-loop amplitude. This allows us to conjecture structures of the correlator/amplitude which should be present at any loop order.

Topics & Concepts