$q\to \infty$ limit of the quasitriangular WZW model

Details $q\to \infty$ limit of the quasitriangular WZW model $q\to \infty$ limit of the quasitriangular WZW model

2006-11-24

arxiv.org/abs/math-ph/0611066v2

J.Nonlin.MathematicalPhys.14:486-518,2007

Physics

Mathematical Physics

final published version, 44 pages, LaTeX, substantial abbreviation, with the review-like first half of the original version su

Scientific paper

We study the $q\to\infty$ limit of the $q$-deformation of the WZW model on a compact simple and simply connected target Lie group. We show that the commutation relations of the $q\to\infty$ current algebra are underlied by certain affine Poisson structure on the group of holomorphic maps from the disc into the complexification of the target group. The Lie algebroid corresponding to this affine Poisson structure can be integrated to a global symplectic groupoid which turns out to be nothing but the phase space of the $q\to\infty$ limit of the $q$-WZW model. We also show that this symplectic grupoid admits a chiral decomposition compatible with its (anomalous) Poisson-Lie symmetries. Finally, we dualize the chiral theory in a remarkable way and we evaluate the exchange relations for the $q\to\infty$ chiral WZW fields in both the original and the dual pictures.

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