Families index theorem in supersymmetric WZW model and twisted K-theory:   The SU(2) case
  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. 
Jouko Mickelsson and Juha-Pekka Pellonp\"a\"a