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

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.

12 pages, harvmac big

References in corpus (6)

• Mirror Symmetry in Generalized Calabi-Yau Compactifications
• Geometric Transitions, Flops and Non-Kahler Manifolds: I
• Geometric Transitions, Flops and Non-Kahler Manifolds: II
• Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds
• Generalised discrete torsion and mirror symmetry for G_2 manifolds
• Fermion BMN operators, the dilatation operator of N=4 SYM, and pp-wave string interactions

Cited by in corpus (3)

• On Mirror Maps for Manifolds of Exceptional Holonomy
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion