The WZW model on Random Regge Triangulations

TL;DR

This paper explores the SU(2) Wess-Zumino-Witten model on triangulated surfaces with variable connectivity, linking quantum field theory, geometry, and algebraic structures through boundary CFT techniques.

Contribution

It introduces a novel characterization of the WZW model on random Regge triangulations using boundary CFT and quantum group techniques, connecting geometry with quantum algebra.

Findings

Partition function expressed via triangulation geometry and 6j symbols.

Boundary operators govern brane-like interactions between curvature and WZW fields.

Connection with bulk Chern-Simons theory briefly discussed.

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.