Generalised discrete torsion and mirror symmetry for G_2 manifolds

Abstract

A generalisation of discrete torsion is introduced in which different discrete torsion phases are considered for the different fixed points or twist fields of a twisted sector. The constraints that arise from modular invariance are analysed carefully. As an application we show how all the different resolutions of the T^7/Z_2^3 orbifold of Joyce have an interpretation in terms of such generalised discrete torsion orbifolds. Furthermore, we show that these manifolds are pairwise identified under G_2 mirror symmetry. From a conformal field theory point of view, this mirror symmetry arises from an automorphism of the extended chiral algebra of the G_2 compactification.

LaTeX, 25 pages, 1 figure; v2: one reference added and comment about higher loop modular invariance corrected, version to be published

References in corpus (2)

• Mirror Symmetry in Generalized Calabi-Yau Compactifications
• Supercoset CFT's for String Theories on Non-compact Special Holonomy Manifolds

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• Four curious supergravities
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• Delta(54) flavor phenomenology and strings
• Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds
• The Topological G2 String
• Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry
• Heterotic strings on G_2 orbifolds
• On Mirror Maps for Manifolds of Exceptional Holonomy
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy
• On the elliptic genera of manifolds of Spin(7) holonomy
• G-structures and Superstrings from the Worldsheet
• Towards A Topological G_2 String
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• BPS branes in discrete torsion orbifolds