CP^n Model on Fuzzy Sphere

Details CP^n Model on Fuzzy Sphere CP^n Model on Fuzzy Sphere

2001-05-10

arxiv.org/abs/hep-th/0105087v3

Nucl.Phys.B625:327-344,2002

Physics

High Energy Physics

High Energy Physics - Theory

v3: 23 pages, Latex. Final version to appear in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(02)00028-7

We construct the CP^n model on fuzzy sphere. The Bogomolny bound is saturated by (anti-)self-dual solitons and the general solutions of BPS equation are constructed. The dimension of moduli space describing the BPS solution on fuzzy sphere is exactly the same as that of the commutative sphere or the (noncommutative) plane. We show that in the soliton backgrounds, the number of zero modes of Dirac operator on fuzzy sphere, Atiyah-Singer index, is exactly given by the topological charge of the background solitons.

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