# A-twisted correlators and Hori dualities

## TL;DR

This paper provides evidence for Hori-Tong and Hori dualities in 2D supersymmetric gauge theories by matching Coulomb branch correlators on Riemann surfaces, including orbifold cases.

## Contribution

It extends duality checks to $O(N)$ theories and their orbifolds by computing and matching Coulomb branch correlators with topological A-twist.

## Key findings

- Correlators match across dual theories for various gauge groups.
- Orbifold $O(N)$ theories are analyzed via twisted boundary conditions.
- Evidence supports the validity of Hori dualities in broader contexts.

## Abstract

The Hori-Tong and Hori dualities are infrared dualities between two-dimensional gauge theories with $\mathcal{N}{=}(2,2)$ supersymmetry, which are reminiscent of four-dimensional Seiberg dualities. We provide additional evidence for those dualities with $U(N_c)$, $USp(2N_c)$, $SO(N)$ and $O(N)$ gauge groups, by matching correlation functions of Coulomb branch operators on a Riemann surface $\Sigma_g$, in the presence of the topological $A$-twist. The $O(N)$ theories studied, denoted by $O_+ (N)$ and $O_- (N)$, can be understood as $\mathbb{Z}_2$ orbifolds of an $SO(N)$ theory. The correlators of these theories on $\Sigma_g$ with $g > 0$ are obtained by computing correlators with $\mathbb{Z}_2$-twisted boundary conditions and summing them up with weights determined by the orbifold projection.