Supersymmetric QFT, Super Loop Spaces and Bismut-Chern Character

TL;DR

This paper provides a quantum interpretation of the Bismut-Chern character form within supersymmetric quantum field theories, linking loop space concepts to differential geometry and constructing related Chern character maps.

Contribution

It introduces a novel quantum perspective on the Bismut-Chern character form using supersymmetric QFTs and develops Chern character maps for these theories.

Findings

Bismut-Chern character arises via loop-deloop process in SUSY QFTs

Quantum interpretation connects loop space lifting to supersymmetric theories

Constructs Chern character maps for SUSY quantum field theories

Abstract

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.