Membrane Scattering in Curved Space with M-Momentum Transfer

TL;DR

This paper investigates membrane scattering in curved space with M-momentum transfer, comparing gauge theory instanton processes with supergravity calculations, revealing differences and discussing their implications for Matrix Theory.

Contribution

It provides a detailed comparison between gauge theory instanton processes and supergravity scattering amplitudes in membrane dynamics, highlighting their differences and the role of cutoff scales.

Findings

Gauge theory and supergravity results differ in membrane scattering.

Cutoff scales of gauge theory and supergravity are complementary.

Supports large-N Matrix Theory conjecture despite differences.

Abstract

We study membrane scattering in a curved space with non-zero M-momentum p_{11} transfer. In the low-energy short-distance region, the membrane dynamics is described by a three-dimensional N=4 supersymmetric gauge theory. We study an n-instanton process of the gauge theory, corresponding to the exchange of n units of p_{11}, and compare the result with the scattering amplitude computed in the low-energy long-distance region using supergravity. We find that they behave differently. We show that this result is not in contradiction with the large-N Matrix Theory conjecture, by pointing out that cutoff scales of the supergravity and the gauge theory are complementary to each other.