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

1991/10/02 by P. Bouwknegt, Peter Bouwknegt, James G. McCarthy +6 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9110007

15 pages

arxiv created 1991/10/02 · openalex publication_date 1991/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Free-field approaches to boundary W [ \widehatg ] (p,p') minimal models
• On the BRST structure of W₃ gravity coupled to c=2 matter

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• Free field realizations in representation theory and conformal field theory
• Drinfeld-Sokolov reduction for quantum groups and deformations of W-algebras
• Free-field approaches to boundary W [ \widehatg ] (p,p') minimal models
• Applications of Free Fields in 2D Current Algebra
• Free field resolution for nonunitary representations of N=2 SuperVirasoro