A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy
Abstract
Starting from the superconformal algebras associated with G2 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 T4 toroidal fibrations. One class of Joyce's orbifolds are pairwise identified under the symmetry.
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