Noncommutative open string, D-brane and duality

We consider open strings ending on D-branes in the presence of constant met ric, G, antisymmetric tensor, B and gauge Field, A. The Hamiltonian is mani festly invariant under a global noncompact group: strikingly similar to tor oidally compactified closed string Hamiltonian. The evolution equations for the string coordinates, {X-i} and their dual partners, {Y-i}, are combined to obtain equations of motion invariant under the noncompact symmetry tran sformations. We show that one can start from a noncommutative theory, with nonvanishing G and B and mixed boundary conditions and then go over to a du al theory whose coordinates obey Dirichlet boundary conditions. It is possi ble to generate B-field by implementing the noncompact symmetry transformat ion. The connection between this duality transformation and Seiberg-Witten map is discussed. (C) 2000 Published by Elsevier Science B.V.