2D Seiberg-like dualities for orthogonal gauge groups

TL;DR

This paper investigates two-dimensional N=(2,2) gauge theories with orthogonal groups, proposing dualities inspired by Seiberg duality and confirming them through elliptic genus calculations.

Contribution

It extends Seiberg-like dualities to 2D orthogonal gauge groups, analyzing different orbifold actions and providing evidence via elliptic genus computations.

Findings

Elliptic genus matches for dual pairs, supporting the proposed dualities.

Distinction between $O(N)_ ext{+}$ and $O(N)_ ext{−}$ theories based on orbifold actions.

Successful extension of duality concepts to 2D orthogonal gauge theories.

Abstract

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 $SO(N) \ltimes Z_2$, 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.