String theory and loop space index theorems
We study index theorems for the Dirac-Ramond operator on a compact Riemannian manifold. The existence of a group action on the loop space makes possible the definition of a character valued index which we calculate by using a two-dimensional sigma model with \(N=1/2\) supersymmetry. We compute the Euler characteristic, the Hirzebruch signature and the Dirac-Ramond genus of loop space. We compare our results to the calculations made by using the Atiyah-Singer character- valued index theorem.
scientific article; zbMATH DE number 4020059
scientific article