Topological vertex for 6d SCFTs with $\mathbb{Z}_2$-twist

TL;DR

This paper calculates the partition functions of 6d $ ext{SO}(2N)$ gauge theories with a $ ext{Z}_2$ twist using topological vertex methods involving O5-planes, confirming results with elliptic genus computations.

Contribution

It introduces a novel topological vertex approach with O5-planes to compute partition functions for twisted 6d gauge theories, extending existing methods.

Findings

Partition functions match elliptic genus results.

Method applies to $SO(8)$ and $SU(3)$ gauge theories.

Validates topological vertex with O5-planes for twisted theories.

Abstract

We compute the partition function for 6d $\mathcal{N}=1$ $SO(2N)$ gauge theories compactified on a circle with $\mathbb{Z}_2$ outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5-planes. As representative examples, we consider 6d $SO(8)$ and $SU(3)$ gauge theories with $\mathbb{Z}_2$ twist. We confirm that these partition functions obtained from the topological vertex with O5-planes indeed agree with the elliptic genus computations.