Discrete gauge symmetries in global intersecting D-brane models constrain theexact form of the perturbative as well as non-perturbative superpotential. Wederive the complete set of conditions on the existence of discrete Zn gaugesymmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional orrigid D6-branes on tilted tori, for which global models of particle physics areknown. Several examples of global left-right symmetric and Pati-Salam modelsare presented. Some discrete `stringy' Zn symmetries are trivial from the fieldtheory point of view, while others have not been identified before.
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