Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-07-23
J.Phys.A36:4191-4206,2003
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, latex. Section 2 is deleted; some clarifications and references added. Final version accepted in J. Phys.A: Math.Gen
Scientific paper
10.1088/0305-4470/36/14/319
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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