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The WZW model on Random Regge Triangulations

G. Arcioni·M. Carfora·C. Dappiaggi·A. Marzuoli
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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}π/3}. We briefly comment on the connection with bulk Chern-Simons theory.

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G. Arcioni, M. Carfora, C. Dappiaggi, A. Marzuoli. 2003-06-13. The WZW model on Random Regge Triangulations. https://doi.org/10.1016/j.geomphys.2004.02.006

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