On the Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere

In the previous papers, we studied the ’t Hooft-Polyakov (TP) monopole configurations in the U(2) gauge theory on the fuzzy 2-sphere, and showed they have nonzero topological charge in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provide a meaning of the projection operator. We further calculate the spectrum of the GW Dirac operator in the TP monopole backgrounds, and confirm the index theorem in these cases. e-mail address: [email protected] e-mail address: [email protected] e-mail address: [email protected] 1