Discrete torsion orbifolds and D-branes II

The consistency of the orbifold action on open strings between D-branes in orbifold theories with and without discrete torsion is analysed carefully. For the example of the C-3 = Z(2) x Z(2) theory, it is found that the consi stency of the orbifold action requires that the D-brane spectrum contains b ranes that give rise to a conventional representation of the orbifold group as well as branes for which the representation is projective. It is also s hown how the results generalise to the orbifolds C-3 = Z(N) x Z(N), for whi ch a number of novel features arise. In particular, the N > 2 theories with minimal discrete torsion have non-BPS branes charged under twisted R-R pot entials that couple to none of the (known) BPS branes.