量子奇点理论中的Virasoro约束
Virasoro constraints in quantum singularity theories
摘要：
对任意Landau-Ginzburg对（W，G）引入Virasoro算子，其中W是非退化的拟齐次多项式，G是某个对角对称群.我们提出了一个猜想，FJRW理论的对（W，G）的总祖先的潜力是由这些Virasoro运营商湮灭。我们证明了这一猜想的各种情形，包括：（1）具有极大群的可逆多项式，（2）具有极小群的二元多项式，（3）具有群的Calabi-Yau多项式。我们还讨论了Virasoro约束，镜像对称的Landau-Ginzburg模型，和Landau-Ginzburg/Calabi-Yau对应之间的联系。
英文摘要：
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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