论文标题
Fermat立方体的较高属FJRW不变性
Higher Genus FJRW Invariants of a Fermat Cubic
论文作者
论文摘要
我们重建了Fermat Cubat Cubat Landau-Ginzburg空间的全部粉丝 - Jarvis-ruan的不变式$（x_1^3+x_2^3+x_3^3：[\ mathbb {c}^3/ \Mathboldμ_3]共同学领域理论。这些属的一个不变体满足了Belusski-Pandharipande关系的奇特方程。它们完全由单个属的不变式确定，可以从三个自旋曲线的模量上的cosection定位和相交理论中获得。我们使用准模型形式的Cayley转换解决了Fermat Cupic Landau-Ginzburg空间的全部兰道甘努格堡/calabi-yau对应关系。这种转变与两种非偏smisimple cohft理论有关：Fermat立方多项式的Fan-Jarvis-Ruan理论和Fermat Cubat Cubic Curve的Gromov-witten理论。结果，可以使用椭圆曲线的gromov-witten不变性计算任何属的粉丝 - 贾维斯 - 鲁恩不变式。他们还满足了包括尸体异常方程和Virasoro约束的精美结构。
We reconstruct the all-genus Fan-Jarvis-Ruan-Witten invariants of a Fermat cubic Landau-Ginzburg space $(x_1^3+x_2^3+x_3^3: [\mathbb{C}^3/ \mathboldμ_3]\to \mathbb{C})$ from genus-one primary invariants, using tautological relations and axioms of Cohomological Field Theories. These genus-one invariants satisfy a Chazy equation by the Belorousski-Pandharipande relation. They are completely determined by a single genus-one invariant, which can be obtained from cosection localization and intersection theory on moduli of three spin curves. We solve an all-genus Landau-Ginzburg/Calabi-Yau Correspondence Conjecture for the Fermat cubic Landau-Ginzburg space using Cayley transformation on quasi-modular forms. This transformation relates two non-semisimple CohFT theories: the Fan-Jarvis-Ruan-Witten theory of the Fermat cubic polynomial and the Gromov-Witten theory of the Fermat cubic curve. As a consequence, Fan-Jarvis-Ruan-Witten invariants at any genus can be computed using Gromov-Witten invariants of the elliptic curve. They also satisfy nice structures including holomorphic anomaly equations and Virasoro constraints.
