Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Florian Hanisch (Potsdam)
We will discuss an approach to integrate differential forms on loop space. Integrals of this type naturally appear within formal path integral proofs of the Atiyah-Singer index theorem and we will discuss how these theorems arise by integrating (even and odd) Bismut Chern characters.
Heuristic arguments moreover suggest that certain integrals of this form should be closely related to Pfaffians. We will show that this realtion does indeed exist if Pfaffians are interpreted in a zeta-renormalised way.