All Higher Genus BPS Membranes in the Plane Wave Background

TL;DR

This paper constructs and analyzes BPS supermembrane solutions in eleven-dimensional plane wave backgrounds, including complex shapes and holes, with matrix regularizations and generalizations to lower BPS states.

Contribution

It provides explicit solutions for higher genus BPS membranes in plane wave backgrounds, extending previous work to arbitrary shapes and holes, and includes matrix regularizations.

Findings

Explicit solutions for supermembranes with arbitrary holes and shapes.

Matrix regularized solutions including fuzzy tori.

Generalization to 1/8 and 1/16 BPS configurations.

Abstract

We consider supermembranes in the maximally supersymmetric plane wave geometry of the eleven dimensions and construct complete solutions of the continuum version of the 1/4 BPS equations. The supermembranes may have an arbitrary number of holes and arbitrary cross sectional shapes. In the matrix regularized version, we solve the matrix equations for several simple cases including fuzzy torus. In addition, we show that these solutions are trivially generalized to 1/8 and 1/16 BPS configuations.