Open Membranes, p-Branes and Noncommutativity of Boundary String Coordinates

TL;DR

This paper investigates the noncommutative properties of boundary string coordinates in an open membrane system with p-branes, using Hamiltonian formalism and gauge choices, suggesting implications for closed string field theory.

Contribution

It introduces a finite chain of constraints for open membranes with cylindrical topology and explores noncommutativity and nonassociativity in boundary string coordinates.

Findings

Finite constraint chain in a suitable gauge

Noncommutative boundary string coordinates

Potential need for noncommutative, nonassociative star product in string field theory

Abstract

We study the dynamics of an open membrane with a cylindrical topology, in the background of a constant three form, whose boundary is attached to p-branes. The boundary closed string is coupled to a two form potential to ensure gauge invariance. We use the action, due to Bergshoeff, London and Townsend, to study the noncommutativity properties of the boundary string coordinates. The constrained Hamiltonian formalism due to Dirac is used to derive the noncommutativity of coordinates. The chain of constraints is found to be finite for a suitable gauge choice, unlike the case of the static gauge, where the chain has an infinite sequence of terms. It is conjectured that the formulation of closed string field theory may necessitate introduction of a star product which is both noncommutative and nonassociative.