On mirror maps for manifolds of exceptional holonomy
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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.
KeywordsString Duality Conformal Field Models in String Theory Superstring Vacua
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- D.D. Joyce, Compact Riemannian 7-manifolds with holonomy g 2. I, J. Diff. Geom.43 (1996) 291.Google Scholar
- D.D. Joyce, Compact Riemannian 7-manifolds with holonomy g 2. II, J. Diff. Geom.43 (1996) 329.Google Scholar
- D.D. Joyce, Compact 8-manifolds with holonomy Spin(7), Inv. Math.123 (1996) 507.Google Scholar
- A. Kovalev, Twisted connected sums and special Riemannian holonomy, J. Reine Angew. Math.565 (2003) 125.Google Scholar
- D. Joyce, Compact manifolds with special holonomy, Oxford mathematical monographs, Oxford University Press, Oxford U.K. (2000).Google Scholar
- C. Vafa, Modular invariance and discrete torsion on orbifolds, Nucl. Phys.B 273 (1986) 592.Google Scholar
- M. Gross, Special Lagrangian Fibrations II: geometry, math/9809072 (1998).
- D. Joyce and S. Karigiannis, A new construction of compact torsion-free G 2-manifolds by gluing families of Eguchi-Hanson spaces, arXiv:1707.09325.