Topological vertex for 6d SCFTs with ℤ2-twist

We compute the partition function for 6d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 1 SO(2N) gauge theories compactified on a circle with ℤ2 outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5-planes. As representative examples, we consider 6d SO(8) and SU(3) gauge theories with ℤ2 twist. We confirm that these partition functions obtained from the topological vertex with O5-planes indeed agree with the elliptic genus computations.