One-loop string corrections to AdS amplitudes from CFT

Abstract

We consider ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$ not considered before.

arXiv comment25 pages. Minor improvements, journal version

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• The Virasoro-Shapiro amplitude in AdS${}_5\times$S${}^5$ and level splitting of 10d conformal symmetry
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals
• On Holography in General Background and the Boundary Effective Action from AdS to dS
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• AdS super gluon scattering up to two loops: A position space approach
• One-loop string corrections for AdS Kaluza-Klein amplitudes
• Notes on gravity multiplet correlators in $Ad{S}_3\times S^3$
• To the cusp and back: Resurgent analysis for modular graph functions
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• One-loop string amplitudes in AdS${}_5\times$S${}^5$: Mellin space and sphere splitting
• Bootstrapping string theory on AdS${}_5\times S^5$
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry