  We show agreements, at one-loop level of field theory, between energies of
semiclassical string states on AdS_5 x S^5/Z_M and anomalous dimensions of
operators in N=0,1,2 orbifold field theories originating from N=4 SYM. On field
theory side, one-loop anomalous dimension matrices can be regarded as
Hamiltonians of spin chains with twisted boundary conditions. These are
solvable by Bethe ansatz. On string side, twisted sectors emerge and we obtain
some string configurations in twisted sectors. In SU(2) subsectors, we compare
anomalous dimensions with string energies and see agreements. We also see
agreements between sigma models of both sides in SU(2) and SU(3) subsectors.
