Topological Actions in Two-Dimensional Quantum Field Thories

Abstract

A systematic approach to 2-dimensional quantum field theories with topological terms in the action is developed using as a mathematical tool the Deligne cohomology. As an application, it is shown how to bosonize the action of free fermions of arbitrary spin on a Riemann surface and how to find the spectrum of the Wess-Zumino-Witten sigma models without recurrence to modular invariance.