Supermembrane on the PP-wave Background

TL;DR

The paper investigates closed and open supermembranes on the eleven-dimensional maximally supersymmetric pp-wave background, deriving the membrane superalgebra via Dirac brackets and identifying central extensions arising from surface terms. It shows that, after discarding central terms, the algebra reduces to the BMN matrix model, while the central charges reveal extended objects such as M2 and M5 branes (and possibly Myers-type effects) in the pp-wave limit. The work also analyzes open membranes, demonstrating that, due to the flux and resulting boundary terms, only $p=1$ boundaries are allowed in this setup unless additional boundary fields are introduced. Overall, the results illuminate how pp-wave backgrounds modify membrane symmetries and boundary conditions, linking membrane theory to BMN Matrix Theory and suggesting directions for covariant formalisms and curved boundary analyses.

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.