The Dirac-Ramond operator for a loop group

Kostant's "cubic" Dirac operator. The Dirac operator on a loop group. Construction of the twisted K-class for a positive energy representation of a loop group, by coupling the Dirac operator to a connection.

References

• Landweber: Multiplets of representations and Kostant's Dirac operator for equal rank loop groups. Duke Math. J. 110 (2001).
• Mickelsson: Gerbes, (twisted) K-theory, and the supersymmetric WZW model. hep-th/0206139.