Compactified D=11 Supermembranes and Symplectic Non-Commutative Gauge Theories

TL;DR

This paper demonstrates that a double compactified D=11 supermembrane with non-trivial wrapping can be described as a symplectic non-commutative gauge theory, revealing deep geometric and algebraic structures.

Contribution

It introduces a formulation of the supermembrane as a symplectic non-commutative gauge theory derived from its minimal Hamiltonian configuration.

Findings

Supermembrane can be described as a symplectic non-commutative gauge theory.

Gauge transformations are generated by area-preserving diffeomorphisms.

The theory corresponds to a symplectic fibration over a Riemann surface.

Abstract

It is shown that a double compactified D=11 supermembrane with non trivial wrapping may be formulated as a symplectic non-commutative gauge theory on the world volume. The symplectic non commutative structure is intrinsically obtained from the symplectic 2-form on the world volume defined by the minimal configuration of its hamiltonian. The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume. Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemman surface with a symplectic connection.