G2 mirrors from Calabi-Yau mirrors

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Abstract
We study the worldsheet CFTs of type II strings on compact G 2 orbifolds obtained as quotients of a product of a Calabi-Yau threefold and a circle. For such models, we argue that the Calabi-Yau mirror map implies a mirror map for the associated G 2 varieties by examining how anti-holomorphic involutions behave under Calabi-Yau mirror symmetry. The mirror geometries identified by the worldsheet CFT are consistent with earlier proposals for twisted connected sum G 2 manifolds.

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