Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case
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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.
Version 2: Essentially simplified proof of the main result using a map from twisted K-theory to gerbes modulo the twisting gerbe; references added + minor corrections
Version 2: Essentially simplified proof of the main result using a map from twisted K-theory to gerbes modulo the twisting gerbe; references added + minor corrections