Generalised twisted partition functions

We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D conformal field theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT. (C) 2001 Elsevier Science B.V. All rights reserved.