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Quantum group generators in conformal field theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jul 1997Embargo end date: 01 Jan 1997Publisher:Elsevier BVJournal:Nuclear Physics B - Proceedings Supplements, volume 56, pages 344-354 (issn: 0920-5632,

Authors: Jens Schnittger; Jens Schnittger;

doi: 10.1016/s0920-5632(97)00345-9 , 10.48550/arxiv.hep-th/9703091

arXiv: http://arxiv.org/abs/hep-th/9703091

Quantum group generators in conformal field theory

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Abstract

These are notes of a seminar given at the 30th International Symposium on the Theory of Elementary Particles, Berlin-Buckow, August 1996. The material is derived from collaborations with E. Cremmer and J.-L. Gervais, and C. Klimcik, and is partially new. Within the general framework of Poisson-Lie symmetry, we discuss two approaches to the problem of constructing moment maps, or q-deformed Noether charges, that generate the quantum group symmetry which appears in many conformal field theories. Concretely, we consider the case of $U_q(sl(2))$ and the operator algebra that describes Liouville theory and other models built from integer powers of screenings in the Coulomb gas picture.

21 pages, LaTeX

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Keywords

High Energy Physics - Theory, Hamiltonian reduction, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Liouville theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, M operator algebra, WZW theory, High Energy Physics - Theory (hep-th), Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Poisson Lie generators, Quantum groups and related algebraic methods applied to problems in quantum theory

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