  We derive the N-point one-loop correlation functions for the currents of an
arbitrary affine Kac-Moody algebra. The one-loop amplitudes, which are elliptic
functions defined on the torus Riemann surface, are specified by group
invariant tensors and certain constant tau-dependent functions. We compute the
elliptic functions via a generating function, and explicitly construct the
invariant tensor functions recursively in terms of Young tableaux. The lowest
tensors are related to the character formula of the representation of the
affine algebra. These general current algebra loop amplitudes provide a
building block for open twistor string theory, among other applications.
