Bootstrapping M-theory Orbifolds

Abstract

We analyze correlation functions of $SU(k)\times SU(2{)}_F$ flavor currents in a family of three-dimensional $\mathcal{N}=4$ superconformal field theories, combining analytic bootstrap methods with input from supersymmetric localization. Via holographic duality, we extract gluon and graviton scattering amplitudes of M-theory on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ which contains a ${\mathbb{C}}^2/{\mathbb{Z}}_k$ orbifold singularity. From these results, we derive aspects of the effective description of M-theory on the orbifold singularity beyond its leading low energy limit. We also determine a threshold correction to the holographic correlator, which vanishes due to equal and opposite contributions from the two-loop gluon and the tree-level bulk graviton exchange.

44 pages plus appendices, v3 typos corrected