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arXiv · 1905.01474

On Mirror Maps for Manifolds of Exceptional Holonomy

Andreas P. Braun·Suvajit Majumder·Alexander Otto
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Abstract

We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups $G_2$ and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to twisted connected sum $G_2$ manifolds, mirrors of such Spin(7) manifolds can be found by applying mirror symmetry to the pair of non-compact manifolds they are glued from. To provide non-trivial checks for such geometric mirror constructions, we give a CFT analysis of mirror maps for Joyce orbifolds in several new instances for both the Spin(7) and the $G_2$ case. For all of these models we find possible assignments of discrete torsion phases, work out the action of mirror symmetry, and confirm the consistency with the geometrical construction. A novel feature appearing in the examples we analyse is the possibility of frozen singularities.

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Andreas P. Braun, Suvajit Majumder, Alexander Otto. 2019-05-04. On Mirror Maps for Manifolds of Exceptional Holonomy. https://doi.org/10.1007/jhep10(2019)204

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