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

P. Bouwknegt·J. McCarthy·K. Pilch
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Abstract

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.

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P. Bouwknegt, J. McCarthy, K. Pilch. 1991-10-02. Some aspects of free field resolutions in 2D CFT with application to the quantum Drinfeld-Sokolov reduction. https://arxiv.org/abs/hep-th/9110007

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