One-loop string corrections to AdS amplitudes from CFT

TL;DR

The study computes α' corrections to the one-loop four-point correlator of the stress-tensor multiplet in $ 4$ SYM at order $1/N^4$, corresponding to string-corrected AdS$_5 imes$S$^5$ amplitudes. It develops a position-space bootstrap using the double discontinuity, revealing a new weight-3 function $f^{(3)}(x,ar{x})$ with novel singularities that completes the one-loop string amplitude ansatz. The authors produce explicit position-space results for $ ext{H}^{(2,3)}$ and $ ext{H}^{(2,5)}$ (and partial $ ext{H}^{(2,6,8,10)}$) and demonstrate consistency with Mellin-space amplitudes, providing a complete classification of ambiguities via polynomial Mellin amplitudes. The work clarifies the analytic structure of AdS loop amplitudes with string corrections and sets the stage for extending the approach to broader correlator families and higher loops.

Abstract

We consider $α'$ 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 $α'$ not considered before.