F-theory Duals of M-theory on G2 Manifolds from Mirror Symmetry

Abstract

Using mirror pairs (M_3, W_3) in type II superstring compactifications on Calabi-Yau threefolds, we study, geometrically, F-theory duals of M-theory on seven manifolds with G_2 holonomy. We first develop a way for getting Landau Ginzburg (LG) Calabi-Yau threefols W_3, embedded in four complex dimensional toric varieties, mirror to sigma model on toric Calabi-Yau threefolds M_3. This method gives directly the right dimension without introducing non dynamical variables. Then, using toric geometry tools, we discuss the duality between M-theory on (S^1 x M_3)/Z_2 with G_2 holonomy and F-theory on elliptically fibered Calabi-Yau fourfolds with SU(4) holonomy, containing W_3 mirror manifolds. Illustrating examples are presented.

25 pages, latex. Section 2 is deleted; some clarifications and references added. Final version accepted in J. Phys.A: Math.Gen. (2003)

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• Relation Between Holonomy Groups in Superstrings, M and F-theories
• Stringy Dyonic Solutions and Clifford Structures
• An N=1 Triality by Spectrum Matching
• NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
• F-theory and N=1 Quivers from Polyvalent Geometry
• On Geometric Transitions in String Compactifications