$G_2$-manifolds from Diophantine equations

TL;DR

This paper links perturbatively flat vacua to M-theory on $G_2$-manifolds, proposing a novel way to classify these manifolds through Diophantine equations, and analyzes warping corrections in flux vacua.

Contribution

It establishes a duality between flat vacua and $G_2$-manifolds, introducing a new method to enumerate $G_2$-manifolds via Diophantine equations and studying warping corrections.

Findings

Perturbatively flat vacua are dual to M-theory on $G_2$-manifolds.

Potential to classify $G_2$-manifolds through solutions to Diophantine equations.

Warping corrections grow at large complex structure but are captured by classical M-theory computations.

Abstract

We argue that perturbatively flat vacua (PFVs) introduced in \cite{Demirtas:2019sip} are dual to M-theory compactifications on $G_2$-manifolds, enabling the enumeration of potentially novel $G_2$-manifolds via solutions to Diophantine equations in type IIB flux quanta. Independently, we show that warping corrections to the effective action of type IIB flux vacua grow parametrically at large complex structure, and we demonstrate that these corrections can nonetheless be captured by a classical geometric computation in M-theory.