# 2d duality for orthogonal gauge theories with 8 supersymmetries

## TL;DR

This paper tests a conjectured duality between two-dimensional orthogonal gauge theories with  supersymmetry by computing and comparing their elliptic genera, considering the effects of global group structure and discrete  parameters.

## Contribution

The paper provides a quantitative test of a new duality conjecture for 2D  orthogonal gauge theories by calculating elliptic genera and analyzing topological sectors.

## Key findings

- Elliptic genera of dual theories match, supporting the conjecture.
- Dependence of sectors on   structure and    parameter is clarified.
- Topological sector analysis confirms the duality's consistency.

## Abstract

We recently conjectured a set of dualities relating two-dimensional orthogonal gauge theories with $\mathcal{N}=(4,4)$ supersymmetry, analogous to Hori's dualities with $\mathcal{N}=(2,2)$ supersymmetry. Here we provide a quantitative test of this conjecture by computing the elliptic genera of the dual pairs and showing that they agree. The elliptic genus of orthogonal gauge theories has multiple topological sectors that depend on the global structure of the group and on the value of a discrete $\theta$ parameter. We derive the dependence on the $\theta$ parameter by determining whether a given sector has $(S)Pin$ structure or not.