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 κ =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 6 j symbols of the quantum group SU(2) Q , at Q= e −1 π/3 . We briefly comment on the connection with bulk Chern–Simons theory.