957 research outputs found
Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
We define the chiral zero modes' phase space of the G=SU(n)
Wess-Zumino-Novikov-Witten model as an (n-1)(n+2)-dimensional manifold M_q
equipped with a symplectic form involving a special 2-form - the Wess-Zumino
(WZ) term - which depends on the monodromy M. This classical system exhibits a
Poisson-Lie symmetry that evolves upon quantization into an U_q(sl_n) symmetry
for q a primitive even root of 1. For each constant solution of the classical
Yang-Baxter equation we write down explicitly a corresponding WZ term and
invert the symplectic form thus computing the Poisson bivector of the system.
The resulting Poisson brackets appear as the classical counterpart of the
exchange relations of the quantum matrix algebra studied previously. We argue
that it is advantageous to equate the determinant D of the zero modes' matrix
to a pseudoinvariant under permutations q-polynomial in the SU(n) weights,
rather than to adopt the familiar convention D=1.Comment: 30 pages, LaTeX, uses amsfonts; v.2 - small corrections, Appendix and
a reference added; v.3 - amended version for J. Phys.
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
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