Journal of High Energy Physics

, 2019:204 | Cite as

On mirror maps for manifolds of exceptional holonomy

  • Andreas P. BraunEmail author
  • Suvajit Majumder
  • Alexander Otto
Open Access
Regular Article - Theoretical Physics


We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups G2 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 G2 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 G2 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.


String Duality Conformal Field Models in String Theory Superstring Vacua 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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© The Author(s) 2019

Authors and Affiliations

  1. 1.Mathematical Institute, University of Oxford Woodstock RoadOxfordU.K.
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  3. 3.Department of PhysicsUniversity of WaterlooWaterlooCanada

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