String corrections to AdS amplitudes and the double-trace spectrum of N=4 SYM

TL;DR

This work analyzes string (α') corrections to four-point, half-BPS correlators in N=4 SYM within AdS5×S5, showing that flat-space limits fix the leading $\lambda^{-3/2}$ Mellin amplitudes for arbitrary external charges. Through a detailed unmixing of double-trace operators, the authors reveal striking patterns in the $\mathcal{N}=4$ SU(4) singlet and $[0,1,0]$ channels, interpreted as traces of a ten-dimensional symmetry. Extending to order $\lambda^{-5/2}$, they reproduce known results for the $\langle O_2 O_2 O_p O_p \rangle$ family and derive new constraints for the $\langle O_2 O_3 O_{p-1} O_p \rangle$ family, validating the 10d-origin picture and guiding higher-order corrections. The results connect flat-space string theory with AdS/CFT data, offering predictive structure for the spectrum and three-point functions dictated by a hidden 10d conformal symmetry. This framework enhances understanding of string corrections in holography and suggests avenues to constrain further subleading contributions via localisation and bulk amplitudes.

Abstract

We consider $α'$ corrections to four-point correlators of half-BPS operators in $\mathcal{N}=4$ super Yang-Mills theory in the supergravity limit. By demanding the correct behaviour in the flat space limit, we find that the leading $(α')^3$ correction to the Mellin amplitude is fixed for arbitrary charges of the external operators. By considering the mixing of double-trace operators we can find the $(α')^3$ corrections to the double-trace spectrum which we give explicitly for $su(4)$-singlet operators. We observe striking patterns in the corrections to the spectra which hint at their common ten-dimensional origin. By extending the observed patterns and imposing them at order $(α')^5$ we are able to reproduce the recently found result for the correction to the Mellin amplitude for $\langle \mathcal{O}_2 \mathcal{O}_2 \mathcal{O}_p \mathcal{O}_p \rangle$ correlators. By applying a similar logic to the $[0,1,0]$ channel of $su(4)$ we are able to deduce new results for the correlators of the form $\langle \mathcal{O}_2 \mathcal{O}_3 \mathcal{O}_{p-1} \mathcal{O}_p \rangle$.