A Scaling Limit With Many Noncommutativity Parameters

TL;DR

This paper derives a worldsheet propagator for open strings with different magnetic fields at each end, leading to a generalized scaling limit involving two noncommutativity parameters, extending noncommutative Yang-Mills theory.

Contribution

It introduces a new scaling limit for open strings with distinct magnetic fields at each end, resulting in a theory with two noncommutativity parameters.

Findings

Derived the worldsheet propagator for open strings with different magnetic fields.

Computed two distinct noncommutativity parameters at each string end.

Generalized the scaling limit to include both noncommutativity parameters.

Abstract

We derive the worldsheet propagator for an open string with different magnetic fields at the two ends, and use it to compute two distinct noncommutativity parameters, one at each end of the string. The usual scaling limit that leads to noncommutative Yang-Mills can be generalized to a scaling limit in which both noncommutativity parameters enter. This corresponds to expanding a theory with U(N) Chan-Paton factors around a background U(1)^N gauge field with different magnetic fields in each U(1).