Quantum groups as generalized gauge symmetries in WZNW models. Part II. The quantized model

Journal Article · Sat Jul 15 04:00:00 EDT 2017 · Physics of Particles and Nuclei

DOI:https://doi.org/10.1134/S1063779617040050· OSTI ID:22979404

This is the second part of a paper dealing with the “internal” (gauge) symmetry of the Wess-Zumino-Novikov-Witten (WZNW) model on a compact Lie group G. It contains a systematic exposition, for G = SU(n), of the canonical quantization based on the study of the classical model (performed in the first part) following the quantum group symmetric approach first advocated by L.D. Faddeev and collaborators. The internal symmetry of the quantized model is carried by the chiral WZNW zero modes satisfying quadratic exchange relations and an n-linear determinant condition. For generic values of the deformation parameter the Fock representation of the zero modes’ algebra gives rise to a model space of U{sub q}(sl(n)). The relevant root of unity case is studied in detail for n = 2 when a “restricted” (finite dimensional) quotient quantum group is shown to appear in a natural way. The module structure of the zero modes’ Fock space provides a specific duality with the solutions of the Knizhnik-Zamolodchikov equation for the four point functions of primary fields suggesting the existence of an extended state space of logarithmic CFT type. Combining left and right zero modes (i.e., returning to the 2D model), the rational CFT structure shows up in a setting reminiscent to covariant quantization of gauge theories in which the restricted quantum group plays the role of a generalized gauge symmetry.

• OSTI ID: 22979404
• Journal Information: Physics of Particles and Nuclei, Journal Name: Physics of Particles and Nuclei Journal Issue: 4 Vol. 48; ISSN 1063-7796
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONFORMAL INVARIANCE
DUALITY
FOCK REPRESENTATION
GAUGE INVARIANCE
LIE GROUPS
MATHEMATICAL SOLUTIONS
QUANTUM FIELD THEORY
QUANTUM GROUPS
SYMMETRY