# Families Index Theorem in Supersymmetric WZW Model and Twisted K-Theory: The SU(2) Case

@article{Mickelsson2005FamiliesIT, title={Families Index Theorem in Supersymmetric WZW Model and Twisted K-Theory: The SU(2) Case}, author={Jouko Mickelsson and Juha-Pekka Pellonp{\"a}{\"a}}, journal={Communications in Mathematical Physics}, year={2005}, volume={271}, pages={775-789} }

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.

## 8 Citations

Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

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- 2012

Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as…

Differential Twisted K-theory and Applications

- Mathematics
- 2007

In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also…

Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class II: Topological and equivariant models

- Mathematics, Physics
- 2012

This is a study of twisted K-theory on a product space $T \times M$. The twisting comes from a decomposable cup product class which applies the 1-cohomology of $T$ and the 2-cohomology of $M$. In the…

O ct 2 00 7 DIFFERENTIAL TWISTED K-THEORY AND APPLICATIONS

- 2008

In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a degree three 3 Deligne cocycle. We also establish the general…

Group Extensions, Gerbes and Twisted K-theory

- Mathematics
- 2008

This thesis reviews the theory of group extensions, gerbes and twisted K-theory. Application to anomalies in gauge theory is briefly discussed. The main results are presented in two appended scient…

Twisted K-Theory and Gerbes from Hamiltonian Quantization

- Physics
- 2013

In this introductory part we review recent progress in the application of the methods of Hamiltonian quantization to construct twisted K-theory elements and gerbes. The important examples are the…

Mickelsson's twisted K-theory invariant and its generalizations

- Mathematics
- 2013

Mickelsson's invariant is an invariant of certain odd twisted K-classes of compact oriented three dimensional manifolds. We reformulate the invariant as a natural homomorphism taking values in a…

Twisted differential cohomology

- MathematicsAlgebraic & Geometric Topology
- 2019

The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it…

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