Open Strings on Orbifolds and Anomaly Analysis.

The consistency of open superstring theory compactified on a Z_2 orbifold is studied. Boundary and cross-cap operators are constructed for the Z _2 orbifold model; and Chan-Paton factors are chosen so that massless sources cancel among the boundary and cross-cap operators. It is argued that this leads to gauge, mixed, and gravitational anomaly cancellation. Anomalous scattering amplitudes relevant to the gauge and mixed gauge/ gravitational anomalies are explicitly calculated and shown to vanish for both the flat space and Z_2 orbifold models. A string theoretic version of Pauli-Villars regulation is used to perform these calculations. The result of attempting to use this method to calculate the gravitational anomaly is indicated; and shortcomings of the regulation scheme are discussed.