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Mirror Symmetry and Landau Ginzburg Calabi-Yau Superpotentials in F-theory Compactifications

Adil Belhaj
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Abstract

We study Landau Ginzburg (LG) theories mirror to 2D N=2 gauged linear sigma models on toric Calabi-Yau manifolds. We derive and solve new constraint equations for Landau Ginzburg elliptic Calabi-Yau superpotentials, depending on the physical data of dual linear sigma models. In Calabi-Yau threefolds case, we consider two examples. First, we give the mirror symmetry of the canonical line bundle over the Hirzebruch surfaces $\bf F_n$. Second, we find a special geometry with the affine so(8) Lie algebra toric data extending the geometry of elliptically fibered K3. This geometry leads to a pure N=1 six dimensional SO(8) gauge model from the F-theory compactification. For Calabi-Yau fourfolds, we give a new algebraic realization for ADE hypersurfaces.

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Adil Belhaj. 2001-12-01. Mirror Symmetry and Landau Ginzburg Calabi-Yau Superpotentials in F-theory Compactifications. https://doi.org/10.1088/0305-4470%2F35%2F4%2F309

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