On Genus-one String Amplitudes on $AdS_5 \times S^5$

TL;DR

This paper analyzes genus-one string amplitudes in AdS_5 x S^5 by studying non-planar correlators in N=4 super-Yang-Mills theory, revealing simplified Mellin space structures that clarify flat space limits and UV divergences.

Contribution

It provides a detailed Mellin space analysis of non-planar correlators at genus one, connecting supergravity and string corrections in AdS/CFT.

Findings

Simplified Mellin space structure of genus-one amplitudes.

Manifestation of flat space limit in Mellin space.

Insights into UV divergence structure at genus one.

Abstract

We study non-planar correlators in ${\cal N}=4$ super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order $1/N^4$ and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on $AdS_5 \times S^5$ in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.