Dirichlet Joyce Manifolds, Discrete Torsion and Duality

TL;DR

This paper explores dualities between Type IIA, Type IIB, and M-theory compactified on Joyce 7-manifolds, revealing new insights into discrete torsion, T-duality, and the broader conjectures connecting these theories.

Contribution

It extends the Papadopoulos-Townsend conjecture by demonstrating dualities involving Joyce manifolds and discrete torsion, and introduces D- and M-manifold descriptions for these compactifications.

Findings

Mapping of Type IIA on Joyce manifolds to D-string configurations in Type IIB.

Duality between Type IIB on Joyce manifolds and M-theory orientifolds with fivebrane sectors.

Proof that discrete torsion affects T-duality relations between Type IIA and IIB theories.

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.