Point-Like Graviton Scattering in Plane-Wave Matrix Model

TL;DR

This paper analyzes point-like graviton scattering in a plane-wave matrix model, revealing a 1/r^7 interaction potential that links the matrix model to eleven-dimensional supergravity.

Contribution

It provides the first computation of graviton scattering in the SO(3) symmetric plane-wave matrix model, highlighting the point-like nature of gravitons and deriving the effective interaction potential.

Findings

Derived a 1/r^7 interaction potential between gravitons.

Showed the scattering behavior is consistent with supergravity predictions.

Demonstrated the point-like graviton solutions differ from membrane solutions in SO(6) space.

Abstract

In a plane-wave matrix model we discuss a two-body scattering of gravitons in the SO(3) symmetric space. In this case the graviton solutions are point-like in contrast to the scattering in the SO(6) symmetric space where spherical membranes are interpreted as gravitons. We concentrate on a configuration in the 1-2 plane where a graviton rotates with a constant radius and the other one elliptically rotates. Then the one-loop effective action is computed by using the background field method. As the result, we obtain the 1/r^7-type interaction potential, which strongly suggests that the scattering in the matrix model would be closely related to that in the light-front eleven-dimensional supergravity.