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The N=2 open string

We show that the N=2 open string describes a theory of self-dual Yang Mills (SDYM) in (2,2) dimensions. The coupling to the closed sector is described by SDYM in a Kahler background, with the Yang-Mills fields providing a source term to the self-duality equation in the gravity sector. The four-point S-matrix elements of the theory vanish, so the tree-level unitarity constraints leading to the Chan-Paton construction are relaxed. By considering more general group-theory ansatze the N=2 string can be written for any gauge group, and not just the classical groups allowed for the bosonic and N=1 strings. Such ad hoc group-theory factors can not be appended to the closed N=2 string, explaining why the Z_n closed N=2 strings are trivial extensions of the Z_1 theory.