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

Abstract

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.

arXiv commentLatex2e, 37 pages, 3 figures

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• Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation
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• Probability distribution over some phenomenological models in the matrix model compactified on a torus
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• The instability of intersecting fuzzy spheres
• Super quantum Dirac operator on the q-deformed super fuzzy sphere in instanton sector using quantum super Ginsparg-Wilson algebra
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