Twisted boundary states in Kazama-Suzuki models
arXiv:hep-th/0306227 · doi:10.1016/j.nuclphysb.2003.11.011
Abstract
We construct Cardy states in the Kazama-Suzuki model G/H x U(1), which satisfy the boundary condition twisted by the automorphisms of the coset theory. We classify all the automorphisms of G/H x U(1) induced from those of the G theory. The automorphism group contains at least a Z_2 as a subgroup corresponding to the charge conjugation. We show that in several models there exist extra elements other than the charge conjugation and that the automorphism group can be larger than Z_2. We give the explicit form of the twisted Cardy states which are associated with the non-trivial automorphisms. It is shown that the resulting states preserve the N=2 superconformal algebra. As an illustration of our construction, we give a detailed study for two hermitian symmetric space models SU(4)/SU(2) x SU(2) x U(1) and SO(8)/SO(6) x U(1) both at level one. We also study the action of the level-rank duality on the Cardy states and find the relation with the exceptional Cardy states originated from a conformal embedding.
39 pages, 5 figures; (v2) references added; (v3) improved argument about automorphism groups of coset theories given, no change in the results
References in corpus (4)
Cited by in corpus (6)
- Level-rank duality of untwisted and twisted D-branes
- Matrix factorisations for rational boundary conditions by defect fusion
- D-branes and matrix factorisations in supersymmetric coset models
- Twisted D-branes of the SU(N)_K WZW model and level-rank duality
- Level-rank duality of untwisted and twisted D-branes of the so(N)_K WZW model
- Fusion of interfaces in Landau-Ginzburg models: a functorial approach