# Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops

## TL;DR

This paper explores mirror symmetry for $G_2$ manifolds created via twisted connected sums, proposing a mirror map analogue and suggesting numerous new dualities in superstring compactifications.

## Contribution

It introduces a mirror map for $G_2$ manifolds from dual pairs of tops, expanding the landscape of known dual superstring backgrounds.

## Key findings

- Formulation of a mirror map for $G_2$ manifolds from dual tops.
- Identification of millions of new dual superstring backgrounds.
- Conjecture of numerous exact dualities among 2d N=1 sigma models.

## Abstract

Recently, at least 50 million of novel examples of compact $G_2$ holonomy manifolds have been constructed as twisted connected sums of asymptotically cylindrical Calabi-Yau threefolds. The purpose of this paper is to study mirror symmetry for compactifications of Type II superstrings in this context. We focus on $G_2$ manifolds obtained from building blocks constructed from dual pairs of tops, which are the closest to toric CY hypersurfaces, and formulate the analogue of the Batyrev mirror map for this class of $G_2$ holonomy manifolds, thus obtaining several millions of novel dual superstring backgrounds. In particular, this leads us to conjecture a plethora of novel exact dualities among the corresponding 2d N=1 sigma models.