Quantum groups as generalized gauge symmetries in WZNW models. Part I. The classical model

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

DOI:https://doi.org/10.1134/S1063779617040049· OSTI ID:22979529

Wess-Zumino-Novikov-Witten (WZNW) models over compact Lie groups G constitute the best studied class of (two dimensional, 2D) rational conformal field theories (RCFTs). A WZNW chiral state space is a finite direct sum of integrable representations of the corresponding affine (current) algebra, and the correlation functions of primary fields are monodromy invariant combinations of left times right sector conformal blocks solving the Knizhnik-Zamolodchikov equation. However, even in this very well understood case of 2D RCFT, the “internal” (gauge) symmetry that governs the ensuing fusion rules remains unclear. On the other hand, the canonical approach to the classical chiral WZNW theory developed by Faddeev, Alekseev, Shatashvili, Gawedzki and Falceto reveals its Poisson-Lie symmetry. After a covariant quantization, the latter gives rise to an associated quantum group symmetry which naturally requires an extension of the state space. This paper contains a review of earlier work on the subject with a special emphasis, in the case G = SU(n), on the emerging chiral “WZNW zero modes” which provide an adequate algebraic description of the internal symmetry structure of the model. Combining further left and right zero modes, one obtains a specific dynamical quantum group, the structure of its Fock representation resembling the axiomatic approach to gauge theories in which a “restricted” quantum group plays the role of a generalized gauge symmetry.

• OSTI ID: 22979529
• 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
CORRELATION FUNCTIONS
CURRENT ALGEBRA
FOCK REPRESENTATION
GAUGE INVARIANCE
LIE GROUPS
QUANTUM FIELD THEORY
QUANTUM GROUPS
SYMMETRY
TWO-DIMENSIONAL CALCULATIONS