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arXiv · 1812.11748

Fukaya category of Landau-Ginzburg model

Huijun Fan·Wenfeng Jiang·Dingyu Yang
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Abstract

This article introduces and provides the mathematical foundation of the open string Floer theory of Landau-Ginzburg model viaWitten equation. We introduce the concept of regular tame exact Landau-Ginzburg system on a noncompact Kaehler manifold, and define the notion of Landau-Ginzburg branes, as the objects of the Fukaya category. The study on Witten equation in our context provides the construction of the Fukaya category of Landau-Ginzburg model which was conjectured to be existed in Gaiotto-Moore-Witten's work [22] and Kapranov-Kontsevich-Soibelman's work [30]. This is the first paper in the series of studies on Landau-Ginzburg models in the contexts of the mirror symmetry and other topics.

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Huijun Fan, Wenfeng Jiang, Dingyu Yang. 2018-12-31. Fukaya category of Landau-Ginzburg model. https://arxiv.org/abs/1812.11748

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