$L^2$-index of the Dirac operator of generalized Euclidean Taub-NUT metrics

Abstract

We compute the axial anomaly for the Taub-NUT metric on $R^4$. We show that the axial anomaly for the generalized Taub-NUT metrics introduced by Iwai and Katayama is finite, although the Dirac operator is not Fredholm. We show that the essential spectrum of the Dirac operator is the whole real line.

8 pages, LaTeX, no figures, submitted to the Proceedings of the Workshop QFEXT'05, Barcelona, Spain