Canonical quantization of the WZW model with defects and Chern-Simons theory

Abstract

We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with $N$ defects on cylinder and phase space of Chern-Simons theory on annulus times $R$ with $N$ Wilson lines, and between phase space of WZW model with $N$ defects on strip and Chern-Simons theory on disc times $R$ with $N+2$ Wilson lines. We obtained also symplectomorphism between phase space of the $N$-fold product of the WZW model with boundary conditions specified by permutation branes, and phase space of Chern-Simons theory on sphere with $N$ holes and two Wilson lines.

26 pages, minor corrections done

References in corpus (4)

• Bi-branes: Target Space Geometry for World Sheet topological Defects
• D-branes in an asymmetric orbifold
• Boundaries, defects and Frobenius algebras
• Symmetry breaking, permutation D-branes on group manifolds: boundary states and geometric description

Cited by in corpus (5)

• Defects, Super-Poincaré line bundle and Fermionic T-duality
• The gauging of two-dimensional bosonic sigma models on world-sheets with defects
• Defects in G/H coset, G/G topological field theory and discrete Fourier-Mukai transform
• Quasi-Hamiltonian bookkeeping of WZNW defects
• On canonical quantization of the gauged WZW model with permutation branes