Operator realization of the SU(2) WZNW model

Details Operator realization of the SU(2) WZNW model Operator realization of the SU(2) WZNW model

1996-02-19

arxiv.org/abs/hep-th/9602101v1

Nucl.Phys. B474 (1996) 497-511

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, LATEX

Scientific paper

10.1016/0550-3213(96)00284-2

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.

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