Supersymmetric Path Integrals (I)

02.11.2017, 16:15  –  Haus 9, Raum 1.10
Forschungsseminar Differentialgeometrie

Florian Hanisch

Integration over the space of superpaths, associated to a Riemannian manifold, plays an important role in the path integral approach to the Atiyah-Singer index theorem. This is indeed equivalent to integration of differential forms on the ordinary loop space and we will discuss the definition and properties of a suitable notion of integral, merging the Bosonic Wiener integral and a Fermionic counterpart. In particular, it allows us to integrate Bismut-Chern characters whose integrals give rise to indices of Dirac operators. If time allows, we will moreover sketch how our integral gives rise to an element in a canonically defined Pfaffian line bundle, making use of a zeta-regularized Pfaffian.