How do field theories detect the torsion in topological modular forms?

2023/03/16 by Berwick-Evans, Daniel
#Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2303.09138

Abstract

We construct deformation invariants of 2|1-dimensional Euclidean field theories valued in a cohomology theory approximating topological modular forms. This implies several results anticipated by Stolz and Teichner and gives the first torsion invariants of field theories valued in π_*\rm TMF. The framework leads to a version of the elliptic Euler class described in terms of field-theoretic data, as well as a partial construction of the supersymmetric sigma model with target a string manifold.

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