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arXiv · 1901.04721

The Chern Character of {\theta}-summable Fredholm Modules over dg Algebras and Localization on Loop Space

Batu Güneysu·Matthias Ludewig
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Abstract

We introduce the notion of a {\vartheta}-summable Fredholm module over a locally convex dg algebra {\Omega} and construct its Chern character as a cocycle on the entire cyclic complex of {\Omega}, extending the construction of Jaffe, Lesniewski and Osterwalder to a differential graded setting. Using this Chern character, we prove an index theorem involving an abstract version of a Bismut-Chern character constructed by Getzler, Jones and Petrack in the context of loop spaces. Our theory leads to a rigorous construction of the path integral for N=1/2 supersymmetry which satisfies a Duistermaat-Heckman type localization formula on loop space.

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Batu Güneysu, Matthias Ludewig. 2019-01-15. The Chern Character of {\theta}-summable Fredholm Modules over dg Algebras and Localization on Loop Space. https://arxiv.org/abs/1901.04721

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