Localization of the BFSS matrix model and three-point amplitude in M-theory

TL;DR

This work develops a direct, nonperturbative handle on M-theory via localization in the BFSS matrix model. By formulating the model on a line segment with carefully chosen boundary terms and an off-shell supersymmetry, the authors reduce the partition function to solutions of the Nahm equation. In the tractable case $N=2$, they show that the classical action vanishes at the localization saddle and the one-loop determinant scales as $p^2$, reproducing the momentum dependence of the 11D gravitons' three-point amplitude. This provides nonperturbative evidence that the BFSS model encodes M-theory physics and establishes a framework to extend to larger matrix sizes and higher-point amplitudes.

Abstract

We apply the localization method to the BFSS matrix model with a particular class of boundary conditions, that is related to a scattering problem of 11-dimensional M-theory. For the boundary condition that corresponds to the three-point amplitude of gravitons, we exactly compute the partition function of the model based on the localization method. We find that the result correctly reproduces the expected momentum dependence of the three point amplitude.