Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation

Details Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation

2009-09-29

arxiv.org/abs/0909.5252v2

Phys.Rev.D80:125006,2009

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, typo corrected, version published in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.80.125006

We construct a topological charge of gauge field configurations on a fuzzy S^2xS^2 by using a Dirac operator satisfying the Ginsparg-Wilson relation. The topological charge defined on the fuzzy S^2xS^2 can be interpreted as a noncommutative (or matrix) generalization of the 2nd Chern character on S^2xS^2. We further calculate the number of chiral zero modes of the Dirac operator in topologically nontrivial gauge configurations. Generalizations of our formulation to fuzzy (S^2)^k are also discussed.

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