  Using holography, we study non-perturbative effects in M-theory on
orientifolds from the analysis of the S^3 partition functions of dual field
theories. We consider the S^3 partition functions of N=4 Yang-Mills theory with
O(n) gauge symmetry coupled to one (anti)symmetric and N_f fundamental
hypermultiplets from the Fermi gas approach. In addition to the worldsheet
instanton and membrane instanton corrections to the grand potential, which are
also present in the U(n) Yang-Mills case, we find that there exist "half
instanton" corrections coming from the effect of orientifold plane.
