Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case
arXiv:hep-th/0509064 · doi:10.1007/s00220-006-0186-y
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 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