Probing non-perturbative effects in M-theory on orientifolds

Using holography, we study non-perturbative effects in M-theory on orientifolds from the analysis of the S3 partition functions of dual field theories. We consider the S3 partition functions of N=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} Yang-Mills theory with O(n) gauge symmetry coupled to one (anti)symmetric and Nf 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.