Mirror symmetry for exceptional unimodular singularities
Mirror symmetry for exceptional unimodular singularities
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DOI：
10.4171/jems/691
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
Changzheng Li;Si Li;Kyoji Saito;Yefeng Shen
中科院分区：
文献类型：
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作者：
Changzheng Li;Si Li;Kyoji Saito;Yefeng Shen
本文证明了关于Landau-Ginzburg B面例外幺模奇点的Saito-Givental理论与关于它们的镜像伙伴的Fan-Jarvis-Ruan-Witten理论之间的镜像对称猜想。在B-方面，我们计算亏格零生成函数的微扰公式的原始形式的前三位作者最近介绍。该计算与A侧FJRW理论中的轨道-Grothendieck-Riemann-Roch和WDVV计算相匹配。通过重建技术建立了所有属的全部数据的一致性。我们的结果建立了第一个例子的LG-LG镜像对称的所有属加权齐次多项式的中心电荷大于1（即包含负度变形参数）。
In this paper, we prove the mirror symmetry conjecture between the Saito-Givental theory of exceptional unimodular singularities on Landau-Ginzburg B-side and the Fan-Jarvis-Ruan-Witten theory of their mirror partners on Landau-Ginzburg A-side. On the B-side, we compute the genus-zero generating function from a perturbative formula of primitive forms introduced by the first three authors recently. This computation matches the orbifold-Grothendieck-Riemann-Roch and WDVV calculations in FJRW theory on the A-side. The coincidence of the full data at all genera is established by reconstruction techniques. Our result establishes the first examples of LG-LG mirror symmetry of all genera for weighted homogeneous polynomials of central charge greater than one (i.e. which contain negative degree deformation parameters).