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arXiv 2012.018512020-12math.DGhep-thmath.AGmath.QA

(0,2) 镜像对称在齐次 Hopf 曲面上的研究

(0,2) Mirror Symmetry on homogeneous Hopf surfaces

Luis Álvarez-Cónsul, Andoni De Arriba de La Hera, Mario Garcia-Fernandez

备注：: 58 pages, improved version. Section 4 has been split into two parts, and a new Section 5.2 has been added. References updated. To appear in the International Mathematics Research Notices

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AI总结：

本文在紧致非凯勒复流形上首次构造了(0,2)镜像对称的例子，利用顶点代数、Bismut平坦度量和拓扑T-对偶，将问题归结为Killing旋量与超共形嵌入的研究。

摘要：

在这项工作中，我们在紧致非凯勒复流形上首次发现了(0,2)镜像对称的例子。为此，我们遵循Borisov的镜像对称方法，使用顶点代数和手性de Rham复形。我们的(0,2)镜像例子由配备Bismut平坦多闭度量的一对Hopf曲面给出。要求几何是齐次的，我们将问题简化为对二次李代数上Killing旋量的研究，以及$N=2$超共形顶点代数嵌入超仿射顶点代数的构造，并结合拓扑T-对偶。

英文摘要：

In this work we find the first examples of (0,2) mirror symmetry on compact non-Kähler complex manifolds. For this we follow Borisov's approach to mirror symmetry using vertex algebras and the chiral de Rham complex. Our examples of (0,2) mirrors are given by pairs of Hopf surfaces endowed with a Bismut-flat pluriclosed metric. Requiring that the geometry is homogeneous, we reduce the problem to the study of Killing spinors on a quadratic Lie algebra and the construction of embeddings of the $N=2$ superconformal vertex algebra in the superaffine vertex algebra, combined with topological T-duality.

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