CPT and other symmetries in string/M theory

We initiate a search for non-perturbative consistency conditions in M theory. Some non-perturbative conditions are already known in type-I theories; we review these and search for others. We focus principally on possible anomalies in discrete symmetries. It is generally believed that discrete symmetries in string theories are gauge symmetries, so anomalies would provide evidence for inconsistencies. Using the orbifold cosmic string construction, we give some evidence that the symmetries we study are gauged. We then search for anomalies in discrete symmetries in a variety of models, both with and without supersymmetry. In symmetric orbifold models we extend previous searches, and show in a variety of examples that all anomalies may be canceled by a Green-Schwarz mechanism. We explore some asymmetric orbifold constructions and again find that all anomalies may be canceled this way. The we turn to type-IIB orientifold models where it is known that even perturbative anomalies are non-universal. In the examples we study, by combining geometric discrete symmetries with continuous gauge symmetries, one may define non-anomalous discrete symmetries already in perturbation theory; in other cases, the anomalies are universal. Finally, we turn to the question of CPT conservation in string/M theory. It is well known that CPT is conserved in all string perturbation expansions; here in a number of examples for which a non-perturbative formulation is available we provide evidence that it is conserved exactly