Stable Solutions of the Double Compactified D=11 Supermembrane Dual

TL;DR

This paper formulates the supersymmetric double compactified D=11 supermembrane as a dual 2-brane with U(1) fields, finds stable solutions, and interprets them geometrically, linking to D=10 Super-Maxwell theory.

Contribution

It introduces a Hamiltonian formulation of the dual supermembrane with stable solutions and a geometric interpretation in terms of U(1) line bundles.

Findings

Stable solutions are identified as local minima of the Hamiltonian.

Solutions carry RR magnetic charges related to the worldvolume vector fields.

The semiclassical approximation reduces to D=10 Super-Maxwell theory.

Abstract

The hamiltonian formulation of the supersymmetric closed 2-brane dual to the double compactified D=11 closed supermembrane is presented. The formulation is in terms of two U(1) vector fields related by the area preserving constraint of the SUSY 2-brane. Stable solutions of the field equations, which are local minima of the hamiltonian, are found. In the semiclassical approximation around the stable solutions the action becomes the reduction of D=10 Super-Maxwell to the worldvolume. The solutions carry RR charges as a type of magnetic charges associated with the worldvolume vector field. The geometrical interpretation of the solution in terms of U(1) line bundles over the worldvolume is obtained.