5 research outputs found
A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model
The canonical quantization of the WZNW model provides a complete set of
exchange relations in the enlarged chiral state spaces that include the Gauss
components of the monodromy matrices. Regarded as new dynamical variables, the
elements of the latter cannot be identified -- they satisfy different exchange
relations. Accordingly, the two dimensional theory expressed in terms of the
left and right movers' fields does not automatically respect monodromy
invariance. Continuing our recent analysis of the problem by gauge theory
methods we conclude that physical states (on which the two dimensional field
acts as a single valued operator) are invariant under the (permuted) coproduct
of the left and right . They satisfy additional constraints fully
described for n=2.Comment: 10 pages, LATEX (Proposition 4.2 corrected, one reference added
Operator realization of the SU(2) WZNW model
Decoupling the chiral dynamics in the canonical approach to the WZNW model
requires an extended phase space that includes left and right monodromy
variables. Earlier work on the subject, which traced back the quantum qroup
symmetry of the model to the Lie-Poisson symmetry of the chiral symplectic
form, left some open questions: - How to reconcile the monodromy invariance of
the local 2D group valued field (i.e., equality of the left and right
monodromies) with the fact that the latter obey different exchange relations? -
What is the status of the quantum group symmetry in the 2D theory in which the
chiral fields commute? - Is there a consistent operator formalism in the chiral
and in the extended 2D theory in the continuum limit? We propose a constructive
affirmative answer to these questions for G=SU(2) by presenting the chiral
quantum fields as sums of chiral vertex operators and q-Bose creation and
annihilation operators.Comment: 18 pages, LATE
Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model
The zero modes' Fock space for the extended chiral WZNW model gives
room to a realization of the Grothendieck fusion ring of representations of the
restricted quantum universal enveloping algebra (QUEA) at an even
(-th) root of unity, and of its extension by the Lusztig operators. It is
shown that expressing the Drinfeld images of canonical characters in terms of
Chebyshev polynomials of the Casimir invariant allows a streamlined
derivation of the characteristic equation of from the defining relations of
the restricted QUEA. The properties of the fusion ring of the Lusztig's
extension of the QUEA in the zero modes' Fock space are related to the braiding
properties of correlation functions of primary fields of the extended
current algebra model.Comment: 36 pages, 1 figure; version 3 - improvements in Sec. 2 and 3:
definitions of the double, as well as R- (and M-)matrix changed to fit the
zero modes' one
Canonical Approach to the Quantum WZNW Model
The canonical approach to the chiral SU(n) WZNW model with a monodromy independent r--matrix is reviewed. Taking the quantum group symmetry of the model (which reflects its classical Poisson--Lie symmetry) as a guiding principle, we derive a complete set of exchange relations in the enlarged chiral phase space that includes the Borel components M \Sigma of the monodromy matrix. Regarded as new dynamical variables the elements of M in the left and right sectors cannot be identified: their Poisson brackets have opposite signs. This is a technical reason why the canonical reduction of the pair of chiral models to a single 2--dimensional theory that involves the left and right movers' fields does not respect the quantum group symmetry. A simple modification of the Poisson brackets which does lead to an SL q (n) invariant model is proven unacceptable as a substitute for the 2D theory. As a way out we suggest a weak form of the monodromy and quantum group invariance of the extended 2D theo..
Canonical approach to the quantum WXNW model
Supported in part by the Bulgarian Foundation for Scientific Research under contract F-404Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal