Evidence for an algebra of $G_2$ instantons II

TL;DR

This paper extends previous research by computing a new $G_2$ instanton partition function, completing the foundational set of such functions for a broad class of $G_2$ manifolds.

Contribution

It introduces a novel computation of a $G_2$ instanton partition function, advancing the understanding of $G_2$ geometry and gauge theory.

Findings

Computed a new $G_2$ instanton partition function

Completed the set of building blocks for $G_2$ instanton functions

Enhanced the mathematical framework for $G_2$ manifolds

Abstract

Building on our previous work [2109.01110], we will compute a new kind of $G_2$ instanton partition function. By doing so, we complete a set of building blocks of the instanton partition function associated with a large class of $G_2$ manifolds.