Covariant phase space approach to noncommutativity in tensile and tensionless open strings

TL;DR

This paper investigates noncommutativity in open strings using the covariant phase space formalism, revealing boundary-localized symplectic structures and noncommutative endpoint coordinates in both tensile and tensionless cases.

Contribution

It provides a unified covariant phase space analysis of noncommutativity in tensile and tensionless open strings, extending previous results to the tensionless regime.

Findings

Boundary symplectic form localizes on string endpoints with background fields.

Endpoint coordinates exhibit noncommutative Poisson algebra.

Results unify noncommutativity descriptions for tensile and tensionless strings.

Abstract

We study noncommutativity in open strings using the covariant phase space formalism. For tensile open strings in a constant Kalb-Ramond background, we show that the (pre)-symplectic current splits into a bulk kinetic term plus an exact boundary term, recovering the Seiberg-Witten noncommutativity parameter. We then extend the analysis to intrinsically tensionless strings. In the absence of background fields, the reduced phase space is degenerate and carries no intrinsic Poisson structure. In the presence of a constant Kalb-Ramond field, the symplectic current localises entirely on the boundary, so that the physical phase space becomes purely boundary-supported and the endpoint coordinates acquire a noncommutative Poisson algebra. Including a boundary gauge-field coupling similarly leads to a boundary symplectic form governed by the effective Born-Infeld combination on the D-brane. Our results provide a unified description of noncommutativity in both tensile and tensionless open strings.