Membrane Fuzzy Sphere Dynamics in Plane-Wave Matrix Model

TL;DR

This paper analyzes the dynamics of membrane fuzzy spheres in the plane-wave matrix model, showing they behave as gravitons with a specific interaction potential at large distances.

Contribution

It computes the one-loop quantum corrections to the interaction of two fuzzy spheres in the plane-wave matrix model, revealing their graviton-like behavior.

Findings

Leading order interaction is proportional to 1/r^7.

Fuzzy spheres behave as giant gravitons and gravitons.

Quantum corrections confirm graviton-like dynamics.

Abstract

In plane-wave matrix model, the membrane fuzzy sphere extended in the SO(3) symmetric space is allowed to have periodic motion on a sub-plane in the SO(6) symmetric space. We consider a background configuration composed of two such fuzzy spheres moving on the same sub-plane and the one-loop quantum corrections to it. The one-loop effective action describing the fuzzy sphere interaction is computed up to the sub-leading order in the limit that the mean distance $r$ between two fuzzy spheres is very large. We show that the leading order interaction is of the 1/r^7 type and thus the membrane fuzzy spheres interpreted as giant gravitons really behave as gravitons.