To tilt or not to tilt: discrete gauge symmetries in global intersecting D-brane models

Discrete gauge symmetries in global intersecting D-brane models constrain the exact form of the perturbative as well as non-perturbative superpotential. We derive the complete set of conditions on the existence of discrete Z(n) gauge symmetries on toroidal orbifolds, T-6/Z(N) and T-6/Z(2) x Z(2M), with fractional or rigid D6-branes on tilted tori, for which global models of particle physics are known. Several examples of global left-right symmetric and Pati-Salam models are presented. Some discrete 'stringy' Z(n) symmetries are trivial from the field theory point of view, while others have not been identified before.