Smearing Effect in Plane-Wave Matrix Model

TL;DR

This paper studies the interaction between flat and fuzzy sphere membranes in a plane-wave matrix model, revealing a unique r^{-3} potential due to smearing effects, suggesting graviton-like behavior.

Contribution

It introduces a novel analysis of membrane interactions in plane-wave backgrounds, highlighting the smearing effect and its impact on the potential's form.

Findings

Interaction potential is of r^{-3} type, not r^{-5}.

Fuzzy sphere membrane behaves like a graviton or giant graviton.

Smearing effect causes the modified interaction potential.

Abstract

Motivated by the usual D2-D0 system, we consider a configuration composed of flat membrane and fuzzy sphere membrane in plane-wave matrix model, and investigate the interaction between them. The configuration is shown to lead to a non-trivial interaction potential, which indicates that the fuzzy sphere membrane really behaves like a graviton, giant graviton. Interestingly, the interaction is of r^{-3} type rather than r^{-5} type. We interpret it as the interaction incorporating the smearing effect due to the fact that the considered supersymmetric flat membrane should span and spin in four dimensional subspace of plane-wave geometry.