A Quantum Mechanical Model of Spherical Supermembranes

TL;DR

This paper develops a quantum mechanical model for spherical supermembranes, identifying their vacua and analyzing effects of supersymmetry, with implications for giant gravitons and Matrix theory.

Contribution

It introduces a superfield-based quantum model of spherical supermembranes and analyzes supersymmetric vacua and instanton effects for different supersymmetry cases.

Findings

Two classical vacua identified: extended and point-like membranes.

Instanton effects lift vacua to massive states in the ${\mathcal N} = 2$ case.

Vacua remain massless in the ${\mathcal N} = 4$ case.

Abstract

We present a quantum mechanical model of spherical supermembranes. Using superfields to represent the cartesian coordinates of the membrane, we are able to exactly determine its supersymmetric vacua. We find there are two classical vacua, one corresponding to an extended membrane and one corresponding to a point-like membrane. For the ${\mathcal N} = 2$ case, instanton effects then lift these vacua to massive states. For the ${\mathcal N} = 4$ case, there is no instanton tunneling, and the vacua remain massless. Similarities to spherical supermembranes as giant gravitons and in Matrix theory on pp-waves is discussed.