$L^2$-index of the Dirac operator of generalized Euclidean Taub-NUT   metrics
  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. 
Sergiu Moroianu, Mihai Visinescu