Bootstrapping M-theory Orbifolds

TL;DR

This paper combines bootstrap and localization techniques to analyze correlation functions in 3D superconformal theories, deriving M-theory scattering amplitudes on orbifold backgrounds and exploring effective descriptions beyond leading order.

Contribution

It introduces a novel approach integrating bootstrap and localization to study M-theory orbifolds, providing new insights into scattering amplitudes and effective theories beyond the low energy limit.

Findings

Extracted gluon and graviton scattering amplitudes from holography.

Derived a threshold correction that cancels out due to opposing contributions.

Enhanced understanding of M-theory on orbifold singularities beyond leading order.

Abstract

We analyze correlation functions of $SU(k) \times SU(2)_F$ flavor currents in a family of three-dimensional ${\cal N}=4$ 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 ${\rm AdS}_4\times S^7/\mathbb{Z}_k$ 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.