We propose a correspondence between vertex operator superalgebras and families of sigma models in which the two structures are related by symmetry properties and a certain reflection procedure. The existence of such a correspondence is motivated by previous work on ${\cal N}=(4,4)$ supersymmetric non-linear sigma models on K3 surfaces, and on a vertex operator superalgebra with Conway group symmetry. Here we present an example of the correspondence for ${\cal N}=(4,4)$ supersymmetric non-linear sigma models on four-tori, and compare it to the K3 case.

中文翻译：

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顶点算子超代数/西格玛模型对应：四环面情况

我们提出了顶点算子超代数和 sigma 模型族之间的对应关系，其中两个结构通过对称属性和一定的反射过程相关联。这种对应的存在是由先前在 K3 表面上的 ${\cal N}=(4,4)$ 超对称非线性 sigma 模型和具有 Conway 群对称性的顶点算子超代数上的工作所推动的。在这里，我们给出了一个在四环上的 ${\cal N}=(4,4)$ 超对称非线性 sigma 模型的对应示例，并将其与 K3 情况进行比较。