Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability

Abstract

How much spectral information is needed to determine the correlation functions of a conformal theory? We study this question in the context of planar supersymmetric Yang-Mills theory, where integrability techniques accurately determine the single-trace spectrum at finite 't Hooft coupling. Corresponding OPE coefficients are constrained by dispersive sum rules, which implement crossing symmetry. Focusing on correlators of four stress-tensor multiplets, we construct combinations of sum rules which determine one-loop correlators, and we study a numerical bootstrap problem that nonperturbatively bounds planar OPE coefficients. We observe interesting cusps at the location of physical operators, and we obtain a nontrivial upper bound on the OPE coefficient of the Konishi operator outside the perturbative regime.

arXiv comment33 pages+ appendices, 15 figures

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• The AdS Virasoro-Shapiro Amplitude
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Bootstrap Method in Theoretical Physics