Twisted boundary states in c=1 coset conformal field theories

We study the mutual consistency of twisted boundary conditions in the coset conformal field theory G/H. We calculate the overlap of the twisted boundary states of G/H with the untwisted ones, and show that the twisted boundary states are consistently defined in the diagonal modular invariant. The overlap of the twisted boundary states is expressed by the branching functions of a twisted affine Lie algebra. As a check of our argument, we study the diagonal coset theory so(2n)_1 \oplus so(2n)_1/so(2n)_2, which is equivalent with the orbifold S^1/\Z_2. We construct the boundary states twisted by the automorphisms of the unextended Dynkin diagram of so(2n), and show their mutual consistency by identifying their counterpart in the orbifold. For the triality of so(8), the twisted states of the coset theory correspond to neither the Neumann nor the Dirichlet boundary states of the orbifold and yield the conformal boundary states that preserve only the Virasoro algebra