Tree Level Supergravity and the Matrix Model

TL;DR

This paper compares Matrix model predictions with supergravity for graviton scattering, clarifies previous discrepancies, and discusses new terms and their relation to nonrenormalization theorems.

Contribution

It corrects earlier claims about graviton scattering predictions and identifies new velocity-dependent terms in the Matrix model not matched by supergravity.

Findings

Matrix model and supergravity agree on three graviton scattering

Certain $v^{2n}$ terms are correctly predicted by the Matrix model

The Matrix model predicts $v^6$ terms in four graviton scattering at three loops

Abstract

It has recently been shown that the Matrix model and supergravity give the same predictions for three graviton scattering. This contradicts an earlier claim in the literature (hep-th/9710174). We explain the error in this earlier work, and go on to show that certain terms in the $n$-graviton scattering amplitude involving $v^{2n}$ are given correctly by the Matrix model. The Matrix model also generates certain $v^6$ terms in four graviton scattering at three loops, which do not seem to have any counterparts in supergravity. The connection of these results with nonrenormalization theorems is discussed.