Defects in G/H coset, G/G topological field theory and discrete Fourier-Mukai transform

Understand

In this paper we construct defects in coset $G/H$ theory.

• Canonical quantization of the gauged WZW model $G/H$ with $N$ defects on a cylinder and a strip is performed and the symplectomorphisms between the corresponding phase spaces and those of double Chern-Simons theory on an annulus and a disc with Wilson lines are established.
• Special attention to topological coset $G/G$ has been paid.
• We prove that a $G/G$ theory on a cylinder with $N$ defects coincides with Chern-Simons theory on a torus times the time-line $R$ with 2N Wilson lines.