2D Seiberg-like dualities for orthogonal gauge groups

We consider the analogue of Seiberg duality for two-dimensional 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} = (2, 2) gauge theory with orthogonal gauge groups and with fundamental chiral multiplets proposed by Hori. Following Hori, when we consider O(k) gauge group as the (semi)-direct product of SO(k) ⋉ Z2, we have to consider two kinds of the theories O±(k) depending on the orbifold action of Z2. We give the evidences for the proposed dualities by working out the elliptic genus of dual pair. The matching of the elliptic genus is worked out perfectly for the proposed dualities.