Open membranes, ribbons and deformed Schild strings

TL;DR

This paper studies how open membranes in a magnetic three-form field transform into tensioned ribbons, leading to a deformed Schild string action and non-local interactions, connecting membrane dynamics with non-commutative string theory.

Contribution

It introduces a model where membranes polarize into ribbons under a magnetic field, deforming the Schild string action and modifying string interactions with phase factors.

Findings

Membranes become ribbon-like in a magnetic field.

String interactions acquire phase factors from ribbon volume.

Reduces to non-commutative loop space in a specific limit.

Abstract

We analyze open membranes immersed in a magnetic three-form field-strength $C$. While cylindrical membranes in the absence of $C$ behave like tensionless strings, when the $C$ flux is present the strings polarize into thin membrane ribbons, locally orthogonal to the momentum density, thus providing the strings with an effective tension. The effective dynamics of the ribbons can be described by a simple deformation of the Schild action for null strings. Interactions become non-local due to the polarization, and lead to a deformation of the string field theory, whereby string vertices receive a phase factor proportional to the volume swept out by the ribbons. In a particular limit, this reduces to the non-commutative loop space found previously.