Families index theorem in supersymmetric WZW model and twisted K-theory
Jouko Mickelsson
TL;DR
This paper reviews how twisted K-theory classes on compact Lie groups can be constructed using the supersymmetric Wess-Zumino-Witten model, highlighting the role of Quillen superconnections and their relation to twisted cohomology.
Contribution
It introduces the use of Quillen superconnections for families of supercharges in the supersymmetric WZW model to construct twisted K-theory classes and relate them to twisted cohomology.
Findings
Construction of twisted K-theory classes via supersymmetric WZW model
Introduction of Quillen superconnection for supercharges
Relation between Chern character and twisted cohomology
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 and the Chern character for the family is given and its relation to twisted cohomology is discussed.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Advanced Topics in Algebra