The families analytic index for $1|1$-dimensional Euclidean field theories

Daniel Berwick-Evans

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arXiv · 2303.09207

The families analytic index for $1|1$-dimensional Euclidean field theories

Daniel Berwick-Evans

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Abstract

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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Daniel Berwick-Evans. 2023-03-16. The families analytic index for $1|1$-dimensional Euclidean field theories. https://arxiv.org/abs/2303.09207

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