M-theory on AdS4 × S7 at 1-loop and beyond

Abstract

Abstract We study graviton scattering on AdS4× S7, which is dual to the stress tensor multiplet four-point function in the maximally supersymmetric 3d U(N)1× U(N)−1 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 AdS4× S7/ℤ2 theory dual to U(N)2× U(N)−2 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 N.