Chern characters for supersymmetric field theories

Berwick-Evans, Daniel¹

¹ Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, United States

Geometry & topology, Tome 27 (2023) no. 5, pp. 1947-1986

Résumé

We construct a map from d|1–dimensional Euclidean field theories to complexified K–theory when d = 1 and complex-analytic elliptic cohomology when d = 2. This provides further evidence for the Stolz–Teichner program, while also identifying candidate geometric models for Chern characters within their framework. The construction arises as a higher-dimensional and parametrized generalization of Fei Han’s realization of the Chern character in K–theory as dimensional reduction for 1|1–dimensional Euclidean field theories. In the elliptic case, the main new feature is a subtle interplay between the geometry of the super moduli space of 2|1–dimensional tori and the derived geometry of complex-analytic elliptic cohomology. As a corollary, we obtain an entirely geometric proof that partition functions of 𝒩 = (0,1) supersymmetric quantum field theories are weak modular forms, following a suggestion of Stolz and Teichner.

Détail

DOI : 10.2140/gt.2023.27.1947

Keywords: elliptic cohomology, topological modular forms, supersymmetric field theories, partition function

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