A scaling limit with many noncommutativity parameters

We derive the worldsheet propagator for an open string with different magne tic fields at the two ends, and use it to compute two distinct noncommutati vity parameters, one at each end of the string, The usual scaling limit tha t leads to noncommutative Yang-Mills can be generalized to a scaling limit in which both noncommutativity parameters enter. This corresponds to expand ing a theory with U(N) Chan-Paton factors around a background U(1)(N) gauge field with different magnetic fields in each U(1). (C) 2001 Elsevier Scien ce B.V, All rights reserved.