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We study the spectral problem of N=4 SYM with gauge group SO(N) and Sp(N). Atthe planar level, the difference to the case of gauge group SU(N) is only dueto certain states being projected out, however at the non-planar level noveleffects appear: While 1/N-corrections in the SU(N) case are always associatedwith splitting and joining of spin chains, this is not so for SO(N) and Sp(N).Here the leading 1/N-corrections, which are due to non-orientable Feynmandiagrams in the field theory, originate from a term in the dilatation operatorwhich acts inside a single spin chain. This makes it possible to test forintegrability of the leading 1/N-corrections by standard (Bethe ansatz) meansand we carry out various such tests. For orthogonal and symplectic gauge groupthe dual string theory lives on the orientifold AdS5xRP5. We discuss variousissues related to semi-classical strings on this background.

On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group