2D Seiberg-like dualities for orthogonal gauge groups

We consider the analogue of Seiberg duality for two-dimensional $N=(2,2)$ gauge theory with orthogonal gauge groups and with fundamental chiral multiplets proposed by Hori. Following Hori, when we consider $O(N)$ gauge group as the (semi)-direct product of $SO(N)⋉Z_2$, we have to consider two kinds of the theories $O(N{)}_{\pm }$ depending on the orbifold action of $Z_2$. 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.