Supersymmetric QFT, Super Loop Spaces and Bismut-Chern Character

Details Supersymmetric QFT, Super Loop Spaces and Bismut-Chern Character Supersymmetric QFT, Super Loop Spaces and Bismut-Chern Character

2007-11-24

arxiv.org/abs/0711.3862v3

Mathematics

Differential Geometry

26 pages, some materials added and some typos are corrected

Scientific paper

In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in the framework of supersymmetric quantum field theories developed by Stolz and Teichner \cite{ST07}. We show that the Bismut-Chern character form comes up via a loop-deloop process when one goes from $1|1$D theory over a manifold down to a $0|1$D theory over its free loop space. Based on our quantum interpretation of the Bismut-Chern character form and Chern character form, we construct Chern character type maps for SUSY QFTs.

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