Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-09-08
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, no figures, uses jheppub.sty. v2: minor typos corrected
Scientific paper
This paper discusses the overlap of the Hori-Vafa formulation of mirror symmetry with some other constructions. We focus on compact Calabi-Yau hypersurfaces \mathcal{M}_G = {G = 0} in weighted complex projective spaces. The Hori-Vafa formalism relates a family {\mathcal{M}_G \in WCP^{m-1}_{Q_1,...,Q_m}[s] | \sum_{i=1}^m Q_i = s} of such hypersurfaces to a single Landau-Ginzburg mirror theory. A technique suggested by Hori and Vafa allows the Picard-Fuchs equations satisfied by the corresponding mirror periods to be determined. Some examples in which the variety \mathcal{M}_G is crepantly resolved are considered. The resulting Picard-Fuchs equations agree with those found elsewhere working in the Batyrev-Borisov framework. When G is an invertible nondegenerate quasihomogeneous polynomial, the Chiodo-Ruan geometrical interpretation of Berglund-Huebsch-Krawitz duality can be used to associate a particular complex structure for \mathcal{M}_G with a particular Kaehler structure for the mirror \widetilde{\mathcal{M}}_G. We make this association for such G when the ambient space of \mathcal{M}_G is CP^2, CP^3, and CP^4. Finally, we probe some of the resulting mirror Kaehler structures by determining corresponding Picard-Fuchs equations.
Doran Charles F.
Garavuso Richard S.
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