F-theory Duals of M-theory on G2 Manifolds from Mirror Symmetry
Abstract
Using mirror pairs (M3, W3) in type II superstring compactifications on Calabi-Yau threefolds, we study, geometrically, F-theory duals of M-theory on seven manifolds with G2 holonomy. We first develop a way for getting Landau Ginzburg (LG) Calabi-Yau threefols W3, embedded in four complex dimensional toric varieties, mirror to sigma model on toric Calabi-Yau threefolds M3. 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 (S1 x M3)/Z2 with G2 holonomy and F-theory on elliptically fibered Calabi-Yau fourfolds with SU(4) holonomy, containing W3 mirror manifolds. Illustrating examples are presented.
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