$1|1$维欧氏域论的族解析指标
The families analytic index for $1|1$-dimensional Euclidean field theories
摘要：
本文构造了一类$1|1$维欧氏域论的${\rm KO}$值族指标.这在Stolz-Teichner程序中实现了一个简化的上循环映射。我们进一步表明，一束自旋流形导致一个家庭的部分定义的$1|1$ -欧几里德域论，产生一个上循环细化的家庭的分析指数。选择的方法的目的是推广到$2|1$维域论，其中类似的结构预计提供一个分析指数值的拓扑模形式。
英文摘要：
We construct a ${\rm KO}$-valued families index for a class of $1|1$-dimensional Euclidean field theories. This realizes a conjectured cocycle map in the Stolz--Teichner program. We further show that a bundle of spin manifolds leads to a family of partially-defined $1|1$-Euclidean field theories, yielding a cocycle refinement of the families analytic index. The methods are chosen with the goal of generalizing to $2|1$-dimensional field theories, where analogous structures are expected to provide an analytic index valued in topological modular forms.
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