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arXiv · 2203.02435

Open FJRW Theory and Mirror Symmetry

Mark Gross·Tyler L. Kelly·Ran J. Tessler
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Abstract

We construct an open enumerative theory for the Landau-Ginzburg (LG) model $(\mathbb{C}^2, \mu_r\times \mu_s, x^r+y^s)$. The invariants are defined as integrals of multisections of a Witten bundle with descendents over a moduli space that is a real orbifold with corners. In turn, a generating function for these open invariants yields the mirror LG model and a versal deformation of it with flat coordinates. After establishing an open topological recursion result, we prove an LG/LG open mirror symmetry theorem in dimension two with all descendents. The open invariants we define are not unique but depend on boundary conditions that, when altered, exhibit wall-crossing phenomena for the invariants. We describe an LG wall-crossing group classifying the wall-crossing transformations that can occur.

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Mark Gross, Tyler L. Kelly, Ran J. Tessler. 2022-03-04. Open FJRW Theory and Mirror Symmetry. https://doi.org/10.2140/gt.2026.30.2779

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