Counting Associatives in Compact $G_2$ Orbifolds

TL;DR

This paper constructs specific compact G2 orbifolds from K3 surfaces, identifies infinitely many associative submanifolds affecting M-theory superpotentials, and explores dualities linking to F-theory and twisted connected sum descriptions.

Contribution

It introduces a new class of compact G2 orbifolds from K3 involutions with infinitely many associative submanifolds, and relates them to dual theories and twisted connected sum models.

Findings

Existence of infinitely many associative submanifolds in a specific G2 orbifold

Duality between M-theory on these orbifolds and F-theory on Calabi-Yau fourfolds

Two different descriptions of the main example as a twisted connected sum

Abstract

We describe a class of compact $G_2$ orbifolds constructed from non-symplectic involutions of K3 surfaces. Within this class, we identify a model for which there are infinitely many associative submanifolds contributing to the effective superpotential of M-theory compactifications. Under a chain of dualities, these can be mapped to F-theory on a Calabi-Yau fourfold, and we find that they are dual to an example studied by Donagi, Grassi and Witten. Finally, we give two different descriptions of our main example and the associative submanifolds as a twisted connected sum.