A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy

TL;DR

This paper explores mirror symmetry in Spin(7) holonomy manifolds by extending superconformal algebras from G2 manifolds and identifying automorphisms as T-dualities on toroidal fibrations.

Contribution

It introduces an extension of superconformal algebras to Spin(7) manifolds and demonstrates mirror symmetry as an automorphism realized through T-dualities.

Findings

Mirror symmetry arises as an automorphism in the extended algebra.

14 types of T-dualities realize the automorphism.

Certain Joyce orbifolds are pairwise identified under this symmetry.

Abstract

Starting from the superconformal algebras associated with $G_2$ manifolds, I extend the algebra to the manifolds with spin(7) holonomy. I show how the mirror symmetry in manifolds with spin(7) holonomy arises as the automorphism in the extended sperconformal algebra. The automorphism is realized as 14 kinds of T-dualities on the supersymmetric $T^4$ toroidal fibrations. One class of Joyce's orbifolds are pairwise identified under the symmetry.