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arXiv · 2111.12162

A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds

Sebastian Boldt·Sergio Luigi Cacciatori·Batu Güneysu
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Abstract

Earlier results show that the N = 1/2 supersymmetric path integral on a closed even dimensional Riemannian spin manifold (X,g) can be constructed in a mathematically rigorous way via Chen differential forms and techniques from non-commutative geometry, if one considers it as a current on the smooth loop space of X. This construction admits a Duistermaat-Heckman localization formula. In this note, fixing a topological spin structure on X, we prove that any smooth family of Riemannian metrics on X canonically induces a Chern-Simons current which fits into a transgression formula for the supersymmetric path integral. In particular, this result entails that the supersymmetric path integral induces a differential topological invariant on X, which essentially stems from the A-hat-genus of X.

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Sebastian Boldt, Sergio Luigi Cacciatori, Batu Güneysu. 2021-11-23. A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds. https://arxiv.org/abs/2111.12162

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