On bosonization of 2d conformal field theories Original Research Article

We show how bosonic (free field) representations for so-called degenerate conformal theories are built by singular vectors in Verma modules. Based on this construction, general expressions of conformal blocks are proposed. As an example, we describe new modules for the SL(2) Wess-Zumino-Witten model. They are, in fact, the simplest nontrivial modules in a full set of bosonized highest weight representations of the ŝl2 algebra. The Verma and Wakimoto modules appear as boundary modules of this set. Our construction also yields a new kind of bosonization in 2d conformal field theories.