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

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  • Gor Sarkissian
  • Department of Mathematical Sciences
  • Centre for Quantum Geometry of Moduli Spaces
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.
Original languageEnglish
JournalNuclear Physics, Section B
Pages (from-to)338-357
Number of pages20
Publication statusPublished - 2011

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