Supermembrane on the PP-wave Background

TL;DR

This paper investigates supermembranes on a maximally supersymmetric pp-wave background, deriving their superalgebra with central extensions and exploring boundary conditions for open membranes, linking to matrix models.

Contribution

It calculates the superalgebra of supermembranes on the pp-wave background, including central extensions, and discusses boundary conditions for open supermembranes, connecting to matrix models.

Findings

Superalgebra with central extensions supports extended objects.

Superalgebra matches Berenstein-Maldacena-Nastase matrix model when central terms are ignored.

Boundary conditions for open supermembranes are elaborated.

Abstract

We study the closed and open supermembranes on the maximally supersymmetric pp-wave background. In the framework of the membrane theory, the superalgebra is calculated by using the Dirac bracket and we obtain its central extension by surface terms. The result supports the existence of the extended objects in the membrane theory in the pp-wave limit. When the central terms are discarded, the associated algebra completely agrees with that of Berenstein-Maldacena-Nastase matrix model. We also discuss the open supermembranes on the pp-wave and elaborate the possible boundary conditions.