Orientifold ABJM matrix model: chiral projections and worldsheet instantons

We study the partition function of the orientifold abjm theory, which is a superconformal chern-simons theory associated with the orthosymplectic supergroup. we find that the partition function associated with any orthosymplectic supergroup can be realized as the partition function of a fermi gas system whose density matrix is identical to that associated with the corresponding unitary supergroup with a projection to the even or odd chirality. furthermore we propose an identity which gives directly all of the gopakumar-vafa invariants for the worldsheet instanton effects in the chirally projected theories.