On Lorentz invariance and supersymmetry of four particle scattering amplitudes in $S^N\R^8$ orbifold sigma model

TL;DR

This paper derives four-particle scattering amplitudes in an $S^N\R^8$ orbifold sigma model, demonstrating Lorentz invariance and supersymmetry, and connecting the model to Matrix string theory.

Contribution

It provides the first direct derivation of four-particle scattering amplitudes from the orbifold sigma model using a recently proposed interaction vertex.

Findings

Amplitudes exhibit Lorentz invariance

Amplitudes preserve supersymmetry

Results support the orbifold model as a low-energy limit of Matrix string theory

Abstract

The $S^N\R^8$ supersymmetric orbifold sigma model is expected to describe the IR limit of the Matrix string theory. In the framework of the model the type IIA string interaction is governed by a vertex which was recently proposed by R.Dijkgraaf, E.Verlinde and H.Verlinde. By using this interaction vertex we derive all four particle scattering amplitudes directly from the orbifold model in the large $N$ limit.