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

Adil Belhaj
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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.

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Adil Belhaj. 2003-02-22. F-theory Duals of M-theory on G2 Manifolds from Mirror Symmetry. https://doi.org/10.1088/0305-4470%2F36%2F14%2F319

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