One-loop string corrections to AdS amplitudes from CFT

TL;DR

This paper computes string corrections to one-loop four-point correlators in N=4 super Yang-Mills, revealing new analytic structures and providing explicit results in position space that complement previous Mellin space analyses.

Contribution

It derives position space results for string-corrected one-loop correlators, uncovering new singularities and transcendental functions, thus advancing understanding of AdS loop amplitudes.

Findings

Identification of a transcendental weight three function with new singularities.

Confirmation of the structure of string-corrected one-loop Mellin amplitudes.

Provision of explicit position space results at previously unexplored orders in α'.

Abstract

We consider $\alpha'$ corrections to the one-loop four-point correlator of the stress-tensor multiplet in $\mathcal{N}=4$ super Yang-Mills at order $1/N^4$. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS$_5\times$S$^5$. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop-amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in $\alpha'$ not considered before.