M-theory on AdS4 × S7 at 1-loop and beyond
Luis F. Alday, Shai M. Chester, Himanshu Raj
Abstract
A bstract We study graviton scattering on AdS 4 × S 7 , 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 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 × S 7 / ℤ 2 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 .