Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-06-28
Nucl.Phys.B846:338-357,2011
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, minor typos corrected, an appendix added, references added
Scientific paper
10.1016/j.nuclphysb.2011.01.013
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. We have shown also that a $G/G$ theory on a strip with $N$ defects coincides with Chern-Simons theory on a sphere times the time-line $R$ with $2N+4$ Wilson lines. This particular example of topological field theory enables us to penetrate into a general picture of defects in semisimple 2D topological field theory. We conjecture that defects in this case described by a 2-category of matrices of vector spaces and that the action of defects on boundary states is given by the discrete Fourier-Mukai transform.
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