Alvarez, Orlando; Killingback, T.-P.; Mangano, Michelangelo; Windey, Paul String theory and loop space index theorems. (English) Zbl 0627.58033 Commun. Math. Phys. 111, 1-10 (1987). 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. Cited in 21 Documents MSC: 58Z05 Applications of global analysis to the sciences 58J20 Index theory and related fixed-point theorems on manifolds Keywords:index theorems; Dirac-Ramond operator PDFBibTeX XMLCite \textit{O. Alvarez} et al., Commun. Math. 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