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. 
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