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

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

2006-10-11

arxiv.org/abs/hep-th/0610125v2

Phys.Rev.D75:085021,2007

Physics

High Energy Physics

High Energy Physics - Theory

Latex2e, 37 pages, 3 figures

Scientific paper

10.1103/PhysRevD.75.085021

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 that 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 also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that the configuration space can be classified into the topological sectors. We further calculate the spectrum of the GW Dirac operator in the TP monopole backgrounds, and consider the index theorem in these cases.

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