Title: F-theory duals of M-theory on<i>G</i><sub>2</sub>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 deve...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.Read More