Symplectic connections, Noncommutative Yang Mills theory and Supermembranes

TL;DR

This paper explores the noncommutative geometry of supermembranes in eleven dimensions, constructing a noncommutative supermembrane action with topological terms via symplectic connections and relating it to traditional formulations.

Contribution

It introduces a geometric framework for noncommutative Yang-Mills theory on symplectic manifolds and applies it to supermembranes, revealing new topological features.

Findings

Disclosed noncommutativity in supermembranes with central charges.

Constructed a noncommutative supermembrane action with topological terms.

Established a relation between noncommutative and ordinary supermembrane actions.

Abstract

In built noncommutativity of supermembranes with central charges in eleven dimensions is disclosed. This result is used to construct an action for a noncommutative supermembrane where interesting topological terms appear. In order to do so, we first set up a global formulation for noncommutative Yang Mills theory over general symplectic manifolds. We make the above constructions following a pure geometrical procedure using the concept of connections over Weyl algebra bundles on symplectic manifolds. The relation between noncommutative and ordinary supermembrane actions is discussed.