Dirichlet Joyce Manifolds, Discrete Torsion and Duality

Abstract

Using U-duality transformations we map perturbative Type IIA string theory compactified on a class of Joyce 7-manifolds to a D-strings on D-manifold description in Type IIB theory. For perturbative Type IIB theory on the same class of Joyce manifolds we use duality transformations to map to an M-theory, M-manifold description, which is an orientifold with fivebrane twisted sectors. D and M-manifold descriptions of discrete torsion are found. For the same class of compactifications we show that Type IIA/IIB theory on a Joyce orbifold without (with) discrete torsion is T-dual to Type IIB/IIA theory on the same orbifold with (without) discrete torsion. For this class of Type II compactifications this proves an extension of the Papadopoulos-Townsend conjecture, which states that the Type IIA and IIB theories compactified on the same Joyce 7-manifold are equivalent. Finally we note that the Papadopoulos-Townsend conjecture is a special case of the Generalised Mirror Conjecture.

22 Pages, Latex

References in corpus (4)

• D-branes and Short Distances in String Theory
• Supersymmetric Cycles in Exceptional Holonomy Manifolds and Calabi-Yau 4-Folds
• Orbifold and Orientifold Compactifications of F-Theory and M-Theory to Six and Four Dimensions
• F Theory Orientifolds, M Theory Orientifolds, and Twisted Strings

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• Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry
• Heterotic strings on G_2 orbifolds
• Marginal deformations of heterotic $G_2$ sigma models
• Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy
• A Mirror Pair of Calabi-Yau Fourfolds in Type II String Theory
• On Mirror Maps for Manifolds of Exceptional Holonomy
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• Odd dimensional analogue of the Euler characteristic
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• A "Periodic Table" for Supersymmetric M-Theory Compactifications