Dual Polyhedra, Mirror Symmetry and Landau-Ginzburg Orbifolds

Details Dual Polyhedra, Mirror Symmetry and Landau-Ginzburg Orbifolds Dual Polyhedra, Mirror Symmetry and Landau-Ginzburg Orbifolds

1995-07-13

arxiv.org/abs/hep-th/9507075v1

Mod.Phys.Lett. A11 (1996) 389-396

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, Latex

Scientific paper

10.1142/S0217732396000436

New geometrical features of the Landau-Ginzburg orbifolds are presented, for models with a typical type of superpotential. We show the one-to-one correspondence between some of the $(a,c)$ states with $U(1)$ charges $(-1,1)$ and the integral points on the dual polyhedra, which are useful tools for the construction of mirror manifolds. Relying on toric geometry, these states are shown to correspond to the $(1,1)$ forms coming from blowing-up processes. In terms of the above identification, it can be checked that the monomial-divisor mirror map for Landau-Ginzburg orbifolds, proposed by the author, is equivalent to that mirror map for Calabi-Yau manifolds obtained by the mathematicians.

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