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

2023/03/16 by Daniel Berwick-Evans, Berwick-Evans, Daniel
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2303.09207

openalex publication_date 2023/03/16 · openalex created_date 2023/03/19 · openalex updated_date 2026/07/28

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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