Generalised discrete torsion and mirror symmetry for G_2 manifolds

TL;DR

This paper introduces a generalized form of discrete torsion for G_2 manifolds, analyzing its constraints and showing how it relates different orbifold resolutions and their mirror symmetries within a conformal field theory framework.

Contribution

It extends discrete torsion concepts to include fixed point-specific phases and demonstrates their role in G_2 mirror symmetry and orbifold resolution interpretations.

Findings

All resolutions of T^7/Z_2^3 orbifold are interpretable via generalized discrete torsion.

G_2 mirror symmetry is realized through automorphisms of the extended chiral algebra.

Constraints from modular invariance are thoroughly analyzed.

Abstract

A generalisation of discrete torsion is introduced in which different discrete torsion phases are considered for the different fixed points or twist fields of a twisted sector. The constraints that arise from modular invariance are analysed carefully. As an application we show how all the different resolutions of the T^7/Z_2^3 orbifold of Joyce have an interpretation in terms of such generalised discrete torsion orbifolds. Furthermore, we show that these manifolds are pairwise identified under G_2 mirror symmetry. From a conformal field theory point of view, this mirror symmetry arises from an automorphism of the extended chiral algebra of the G_2 compactification.