Topological vertex formalism with O5-plane

TL;DR

This paper introduces a novel topological vertex formalism for Type IIB $(p,q)$ 5-brane webs with O5-planes, enabling computation of topological string partition functions for certain 5d gauge theories and matching known results.

Contribution

It develops a new topological vertex formalism tailored for 5-brane webs with O5-planes, extending computational tools in topological string theory.

Findings

Successfully computes partition functions for 5d $ ext{Sp}(1)$ theories with various flavors.

Matches known results for $N_f=0,1$ cases, validating the formalism.

Provides a new simple expression for the $N_f=8$ case related to E-string theory.

Abstract

We propose new topological vertex formalism for Type IIB $(p,q)$ 5-brane web with an O5-plane. We apply our proposal to 5d $\mathcal{N}=1$ Sp(1) gauge theory with $N_f=0,1,8$ flavors to compute the topological string partition functions and check the agreement with the known results. Especially for the $N_f=8$ case, which corresponds to E-string theory on a circle, we obtain a new, yet simple, expression of the partition function with two Young diagram sum.