A Scaling Limit With Many Noncommutativity Parameters

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).