Twisted boundary conditions in conformally invariant theories

We obtain the free energy f for a U(1)-invariant conformal 2D theory on a cylinder with arbitrarily twisted boundary conditions. Our result is f=-π(c-24Δθ)/6L, where c is the central charge and Δθ is the conformal weight of the operator which realizes the twist by the angle θ. As examples of the general formula, the free chiral massless field and the massless Thirring model are worked out in detail. As an application, we identify the proper twist operator, in the scaling limit, of the XXZ quantum spin chain. (orig.)