M-theory on $AdS_4\times S^7$ at 1-loop and beyond

TL;DR

This paper computes 1-loop corrections to graviton scattering in AdS4xS7, matches flat space limits with M-theory, and uses localization to determine OPE coefficients, advancing understanding of holographic correlators in M-theory.

Contribution

It provides the first detailed 1-loop correction calculations for the AdS4xS7 background and connects these with M-theory S-matrix and localization results, revealing new insights into holographic correlators.

Findings

1-loop corrections match 11d M-theory S-matrix in flat space limit

All 1-loop contact terms vanish according to localization

OPE coefficients saturate bootstrap bounds for all N

Abstract

We study graviton scattering on $AdS_4\times S^7$, 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 $AdS_4\times S^7/\mathbb{Z}_2$ 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 $N$.