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 of obtaining Landau–Ginzburg (LG) Calabi–Yau threefolds W3, embedded in four complex-dimensional toric varieties, mirror to the 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 × M3/Z2 with G2 holonomy and F-theory on elliptically fibred Calabi–Yau fourfolds with SU(4) holonomy, containing W3 mirror manifolds. Illustrative examples are presented.
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