Consistency of orbifolds

Modular invariance is a necessary condition for the consistency of any clos ed string theory. In particular, it imposes stringent constraints on the sp ectrum of orbifold theories, and in principle determines their spectrum uni quely up to discrete torsion classes. In practice, however, there are often ambiguities in the construction of orbifolds that are a consequence of the fact that the action of the orbifold elements on degenerate ground states is not unambiguous. We explain that there exists an additional consistency condition, related to the spectrum of D-branes in the theory, which elimina tes these ambiguities. For supersymmetric orbifolds this condition turns ou t to be equivalent to the condition that supersymmetry is unbroken in the t wisted sectors, but for non-supersymmetric orbifolds it appears to be a gen uinely new consistency condition. (C) 2000 Elsevier Science B.V. All rights reserved.