Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case

: Mickelsson J, Pellonpaa JP

Publisher: SPRINGER

: 2007

: Communications in Mathematical Physics

: COMMUNICATIONS IN MATHEMATICAL PHYSICS

: COMMUN MATH PHYS

: 271

: 3

: 775

: 789

: 15

: 0010-3616

DOI: https://doi.org/10.1007/s00220-006-0186-y

The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Wittenmodel 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.