F-theory Duals of M-theory on G2 Manifolds from Mirror Symmetry

TL;DR

This paper explores the geometric duality between M-theory on G_2 manifolds and F-theory on elliptically fibered Calabi-Yau fourfolds, using mirror symmetry and toric geometry to construct explicit examples.

Contribution

It introduces a new method for deriving Landau Ginzburg Calabi-Yau threefolds mirror to toric Calabi-Yau threefolds, facilitating the study of G_2 duals in F-theory.

Findings

Developed a direct method for obtaining LG Calabi-Yau threefolds

Established duality between M-theory on G_2 manifolds and F-theory on elliptic CY fourfolds

Presented explicit examples illustrating the duality

Abstract

Using mirror pairs (M_3, W_3) in type II superstring compactifications on Calabi-Yau threefolds, we study, geometrically, F-theory duals of M-theory on seven manifolds with G_2 holonomy. We first develop a way for getting Landau Ginzburg (LG) Calabi-Yau threefols W_3, embedded in four complex dimensional toric varieties, mirror to sigma model on toric Calabi-Yau threefolds M_3. This method gives directly the right dimension without introducing non dynamical variables. Then, using toric geometry tools, we discuss the duality between M-theory on (S^1 x M_3)/Z_2 with G_2 holonomy and F-theory on elliptically fibered Calabi-Yau fourfolds with SU(4) holonomy, containing W_3 mirror manifolds. Illustrating examples are presented.