On bosonization of 2d conformal field theories

TL;DR

This paper develops a new bosonization method for 2D conformal field theories using singular vectors in Verma modules, leading to explicit conformal block expressions and novel modules for the SL(2) WZW model.

Contribution

It introduces a new bosonization approach based on singular vectors, providing explicit conformal blocks and constructing new modules for the SL(2) WZW model.

Findings

New modules for the SL(2) WZW model are described.

General expressions for conformal blocks are proposed.

A novel bosonization technique in 2D conformal field theories is introduced.

Abstract

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 non-trivial modules in a full set of bosonized highest weight representations of $\hat {sl}_2$ 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.