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 Ocneanuʹs algebraic construction, and might offer a new route to the study of properties of CFT.