Consistency of orbifolds

Modular invariance is a necessary condition for the consistency of any closed string theory. In particular, it imposes stringent constraints on the spectrum of orbifold theories, and in principle determines their spectrum uniquely 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 eliminates these ambiguities. For supersymmetric orbifolds this condition turns out to be equivalent to the condition that supersymmetry is unbroken in the twisted sectors, but for non-supersymmetric orbifolds it appears to be a genuinely new consistency condition.