Construction of All WZW Orbifold Actions

In terms of group orbifold elements with definite monodromy, we give a construction for the action functionals of the twisted sectors of all WZW orbifolds. Surprisingly, locality of the theory dictates a form of the general twisted current algebra in which the twisted right and left mover current algebras are not a priori copies of each other. For the permutation orbifolds and the inner-automorphic orbifolds we are able to show by a mode relabelling that the situation is equivalent to copies, but we do not have an argument that this is always the case. In an extension, we also construct the actions for all the orbifolds of any nonlinear sigma model with a symmetry which acts linearly on the coordinates. Finally, implications for orbifold conformal field theory are discussed, including a conjectured set of orbifold Einstein equations for those sigma model orbifolds in this class which are also 1-loop conformal