The Algebra & Geometry of Modern Physics

I will discuss various relations between CS and WZW theories at classical level. First, I show how the Wess-Zumino term arises as a gauge variation of Chern-Simons action, in case the three-manifold has a boundary. The main topic, however, will be to derive an equivalence between classical phase spaces of CS and WZW theories, following https://arxiv.org/abs/hep-th/0101170v1. The WZW model will be defined on a strip with "untwisted" boundary conditions while the corresponding CS theory lives on (disc x line) with two Wilson lines (in representations determined by boundary conditions at both ends of the strip) puncturing the disc. Brief comments about quantization might be mentioned if time allows.