Q->infinite limit of the quasitriangular WZW model

DOI

10.2991/jnmp.2007.14.4.1How to use a DOI?

Abstract

We study the 'q-> infinite' limit of the q-deformation of the WZW model on a compact simple and simply connected target Lie group. We show that the commutation rela- tions of the 'q -> infinite' 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 inte- grated to a global symplectic groupoid which turns out to be nothing but the phase space of the 'q -> infinite' 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 -> infinite' chiral WZW fields in both the original and the dual pictures.

Copyright

© 2007, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Ctirad Klimčík
PY  - 2007
DA  - 2007/12/01
TI  - Q->infinite limit of the quasitriangular WZW model
JO  - Journal of Nonlinear Mathematical Physics
SP  - 494
EP  - 526
VL  - 14
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2007.14.4.1
DO  - 10.2991/jnmp.2007.14.4.1
ID  - Klimčík2007
ER  -