Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case

TL;DR

This paper explores the connection between supersymmetric WZW models and twisted K-theory on SU(2), using superconnections to explicitly compute the Chern character and analyze its localization on D-branes.

Contribution

It introduces a superconnection approach to construct twisted K-theory classes in supersymmetric WZW models, with explicit calculations for SU(2).

Findings

Explicit Chern character computation for SU(2).

Localization of the character form on D-branes.

Framework linking supersymmetric models to twisted K-theory.

Abstract

The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a compact Lie group and the Chern character is explicitly computed in the case of SU(2). For large euclidean time, the character form is localized on a D-brane.