5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories

TL;DR

This paper constructs 5-brane web configurations for 5d $ ext{G}_2$ gauge theories, including pure and flavored cases, and computes their partition functions, confirming consistency with existing results.

Contribution

It introduces novel 5-brane web constructions for 5d $ ext{G}_2$ gauge theories derived from Higgsing $SO(7)$, and applies topological vertex methods to compute their partition functions.

Findings

Constructed 5-brane webs for pure and flavored 5d G2 theories.

Computed partition functions matching known results.

Demonstrated the use of O5-plane configurations in web constructions.

Abstract

We propose 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories. From a Higgsing of the $SO(7)$ gauge theory with a hypermultiplet in the spinor representation, we construct two types of 5-brane web configurations for the pure $G_2$ gauge theory using an O5-plane or an $\widetilde{\text{O5}}$-plane. Adding flavors to the 5-brane web for the pure $G_2$ gauge theory is also discussed. Based on the obtained 5-brane webs, we compute the partition functions for the 5d $G_2$ gauge theories using the recently suggested topological vertex formulation with an O5-plane, and we find agreement with known results.