One-Loop Flatness of Membrane Fuzzy Sphere Interaction in Plane-Wave Matrix Model

TL;DR

This paper investigates the quantum stability and interaction potential of membrane fuzzy spheres in a plane-wave matrix model, revealing a flat effective potential indicating no force between the spheres.

Contribution

It demonstrates that fuzzy spheres are stable under quantum corrections and that their interaction potential is flat, suggesting no force between them in this model.

Findings

Fuzzy spheres are stable under quantum corrections.

The effective potential between fuzzy spheres is flat.

No force acts between the fuzzy spheres at one-loop level.

Abstract

In the plane-wave matrix model, the background configuration of two membrane fuzzy spheres, one of which rotates around the other one in the SO(6) symmetric space, is allowed as a classical solution. We study the one-loop quantum corrections to this background in the path integral formulation. Firstly, we show that each fuzzy sphere is stable under the quantum correction. Secondly, the effective potential describing the interaction between fuzzy spheres is obtained as a function of r, which is the distance between two fuzzy spheres. It is shown that the effective potential is flat and hence the fuzzy spheres do not feel any force. The possibility on the existence of flat directions is discussed.