Open descendants of U(2N) orbifolds at rational radii

We construct explicitly the open descendants of some exceptional automorphism invariants of U(2N) orbifolds. We focus on the case N = p1 × p2, p1 and p2 prime, and on the automorphisms of the diagonal and charge conjugation invariants that exist for these values of N. These correspond to orbifolds of the circle with radius R 2 = 2p1/p2. For each automorphism invariant we find two consistent Klein bottles, and for each Klein bottle we find a complete (and probably unique) set of boundary states. The two Klein bottles are in each case related to each other by simple currents, but surprisingly for the automorphism of the charge conjugation invariant neither of the Klein bottle choices is the canonical (symmetric) one.