Summary: | <p>We study graviton scattering on <em>AdS<sup>4</sup></em> × <em>S<sup>7</sup></em>, which is dual to the stress tensor multiplet four-point function in the maximally supersymmetric 3d U(<em>N</em>)<sub>1</sub> × U(<em>N</em>)<sub>−1</sub> ABJM theory. We compute 1-loop corrections to this holographic correlator coming from Witten diagrams with supergravity R and higher derivative R4 vertices, up to contact term ambiguities, and find that the flat space limit matches the corresponding terms in the 11d M-theory S-matrix. We then use supersymmetric localization to show that all the 1-loop contact terms vanish, as was previously observed for the <em>AdS<sup>4</sup></em> × <em>S<sup>7</sup></em>/ℤ<sub>2</sub> theory dual to U(<em>N</em>)<sub>2</sub> × U(<em>N</em>)<sub>−2</sub> ABJM. Finally, we use the recent localization results of Gaiotto and Abajian, as inspired by twisted M-theory, to compute all the short OPE coefficients in correlators of the stress tensor multiplet and the next lowest half-BPS operator, which we find saturate the bootstrap bounds on these mixed correlators for all <em>N</em>.</p>
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