The WZW model on Random Regge Triangulations
Abstract
By exploiting a correspondence between Random Regge triangulations (i.e., Regge triangulations with variable connectivity) and punctured Riemann surfaces, we propose a possible characterization of the SU(2) Wess-Zumino-Witten model on a triangulated surface of genus g. Techniques of boundary CFT are used for the analysis of the quantum amplitudes of the model at level k=1. These techniques provide a non-trivial algebra of boundary insertion operators governing a brane-like interaction between simplicial curvature and WZW fields. Through such a mechanism, we explicitly characterize the partition function of the model in terms of the metric geometry of the triangulation, and of the 6j symbols of the quantum group SU(2)_Q, at Q=e^{\sqrt{-1}\pi /3}. We briefly comment on the connection with bulk Chern-Simons theory.
Cite
@article{arxiv.hep-th/0209031,
title = {The WZW model on Random Regge Triangulations},
author = {G. Arcioni and M. Carfora and C. Dappiaggi and A. Marzuoli},
journal= {arXiv preprint arXiv:hep-th/0209031},
year = {2015}
}
Comments
44 pages. This is a vastly revised version of a characterization of SU(2) WZW model on a metrically triangulated surface that we posted in a preliminary version a few months ago