Some aspects of free field resolutions in 2D CFT with application to the quantum Drinfeld-Sokolov reduction

Bouwknegt, P.; McCarthy, J.; Pilch, K.

Some aspects of free field resolutions in 2D CFT with application to the quantum Drinfeld-Sokolov reduction

Authors

Bouwknegt, P.

McCarthy, J.

Pilch, K.

Description

We review some aspects of the free field approach to two-dimensional conformal field theories. Specifically, we discuss the construction of free field resolutions for the integrable highest weight modules of untwisted affine Kac-Moody algebras, and extend the construction to a certain class of admissible highest weight modules. Using these, we construct resolutions of the completely degenerate highest weight modules of W-algebras by means of the quantum Drinfeld-Sokolov reduction. As a corollary we derive character formulae for these degenerate highest weight modules.
15 pages