Coupling of open to closed bosonic strings in four dimensions

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We study the construction of D < 26 open bosonic string theories using the fermionic formulation for the internal degrees of freedom. The various models are specified by the boundary conditions of the world sheet fermions on the annulus. Using the fact that open string loops can be transformed into closed string exchanges, we determine possible open string models which may be coupled to known D < 26 closed string models. Finally, as a verification of consistency, we examine particular open string non-planar amplitudes.