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arXiv · 2103.00313

Virasoro constraints in quantum singularity theories

Weiqiang He·Yefeng Shen
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Abstract

We introduce Virasoro operators for any Landau-Ginzburg pair (W, G) where W is a non-degenerate quasi-homogeneous polynomial and G is a certain group of diagonal symmetries. We propose a conjecture that the total ancestor potential of the FJRW theory of the pair (W,G) is annihilated by these Virasoro operators. We prove the conjecture in various cases, including: (1) invertible polynomials with the maximal group, (2) some two-variable polynomials with the minimal group, (3) certain Calabi-Yau polynomials with groups. We also discuss the connections among Virasoro constraints, mirror symmetry of Landau-Ginzburg models, and Landau-Ginzburg/Calabi-Yau correspondence.

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Weiqiang He, Yefeng Shen. 2021-02-27. Virasoro constraints in quantum singularity theories. https://arxiv.org/abs/2103.00313

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