Four graviton scattering amplitude from $S^N\large{\bf R}^{8}$ supersymmetric orbifold sigma model

TL;DR

This work demonstrates that the four-graviton scattering amplitude in type II string theory can be derived from the IR description of Matrix theory as an $S^N{\bf R}^8$ supersymmetric orbifold sigma model perturbed by the DVV interaction vertex. By constructing invariant twisted-sector vertex operators, employing the stress-energy tensor method, and carefully normalizing bosonic and fermionic correlators, the authors obtain a Lorentz-invariant amplitude that matches the conventional string result in the large-$N$ limit. The approach leverages the nonabelian orbifold structure, bosonization in SU(4)×U(1), and a detailed analysis of monodromies and structure constants to reproduce the standard open-string kinematic factor. This provides strong evidence that the two-dimensional Yang–Mills description captures nonperturbative string dynamics and opens routes to loop amplitudes and heterotic generalizations within the orbifold sigma-model framework.

Abstract

In the IR limit the Matrix string theory is expected to be described by the $S^N\R^{8}$ supersymmetric orbifold sigma model. Recently Dijkgraaf, Verlinde and Verlinde proposed a vertex that may describe the type IIA string interaction. In this paper using this interaction vertex we derive the four graviton scattering amplitude from the orbifold model in the large $N$ limit.

Figures (2)

• Figure 1: The diagramm representation of different correlation functions in eq.(4.32)
• Figure 2: The $N$-fold covering of the $z$-sphere by the $t$-sphere.