Twisted boundary states in Kazama-Suzuki models

We construct Cardy states in the Kazama-Suzuki model G/H×U(1), which satisfy the boundary condition twisted by the automorphisms of the coset theory. We classify all the automorphisms of G/H×U(1) induced from those of the G theory. The automorphism group contains at least a ℤ₂ 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 ℤ₂. 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)×SU(2)×U(1) and SO(8)/SO(6)×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.