Kac-Moody and Virasoro Characters from the Perturbative Chern-Simons Path Integral

Understand

We evaluate to one loop the functional integral that computes the partition functions of Chern-Simons theories based on compact groups, using the background field method and a covariant gauge fixing.

• We compare our computation with the results of other, less direct methods.
• We find that our method correctly computes the characters of irreducible representations of Kac-Moody algebras.
• To extend the computation to non-compact groups we need to perform an appropriate analytic continuation of the partition function of the compact group.