Current Algebra on the Torus

Understand

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.