6d (2,0) and M-theory at 1-loop

Abstract

We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric $(2,0)$ $A_{N-1}$ and $D_N$ theories, which have no Lagrangian description, but in the large $N$ limit are holographically dual to weakly coupled M-theory on $Ad{S}_7\times S^4$ and $Ad{S}_7\times S^4/{\mathbb{Z}}_2$, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity $R$ and the first higher derivative correction $R^4$ vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.

arXiv comment35 pages plus appendices, v4 typos corrected, accepted to JHEP

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• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
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• Pure anti-de Sitter supergravity and the conformal bootstrap
• Holographic S-fold theories at one loop
• Bootstrapping (D, D) Conformal Matter
• Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Superconformal blocks in diverse dimensions and $BC$ symmetric functions
• Instanton Worldlines in Five-Dimensional $\Omega$-Deformed Gauge Theory
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories