M-theory on $Ad{S}_4\times S^7$ at 1-loop and beyond

Abstract

We study graviton scattering on $Ad{S}_4\times S^7$, which is dual to the stress tensor multiplet four-point function in the maximally supersymmetric 3d $U(N{)}_1\times U(N{)}_{-1}$ ABJM theory. We compute 1-loop corrections to this holographic correlator coming from Witten diagrams with supergravity $R$ and higher derivative $R^4$ 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 $Ad{S}_4\times S^7/{\mathbb{Z}}_2$ theory dual to $U(N{)}_2\times U(N{)}_{-2}$ 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 $N$.

20 pages, 2 figures, sequel to arXiv:2107.10274, v2 submitted to JHEP