The AdS Virasoro-Shapiro Amplitude

TL;DR

This paper develops a systematic method to compute the AdS Virasoro-Shapiro amplitude, incorporating curvature corrections order by order, and matches known supergravity and integrability results while providing new data for planar N=4 SYM.

Contribution

A constructive, order-by-order approach to calculating the AdS Virasoro-Shapiro amplitude using world-sheet integrals and symmetry constraints, extending previous results.

Findings

Explicit first two curvature corrections computed.

Reproduces all known localization and integrability results.

Provides new CFT data for planar N=4 SYM at strong coupling.

Abstract

We present a constructive method to compute the AdS Virasoro-Shapiro amplitude, order by order in AdS curvature corrections. At kth order the answer takes the form of a genus zero world-sheet integral involving weight 3k single-valued multiple polylogarithms. The coefficients in our ansatz are fixed, order by order, by requiring: crossing symmetry; the correct supergravity limit; the correct structure of poles, determined by dispersive sum rules; and the dimensions of the first few Konishi-like operators, available from integrability. We explicitly construct the first two curvature corrections. Our final answer then reproduces all localisation results and all CFT data available from integrability, to this order, and produces a wealth of new CFT data for planar N=4 SYM at strong coupling.