O(3) Sigma model with Hopf term on Fuzzy Sphere

Details O(3) Sigma model with Hopf term on Fuzzy Sphere O(3) Sigma model with Hopf term on Fuzzy Sphere

2002-11-27

arxiv.org/abs/hep-th/0211258v2

Nucl.Phys. B655 (2003) 300-312

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, Latex, typos corrected, added one reference, to appear in Nucl. Phys. B Reprt-no: IMSc/2002/11/39

Scientific paper

10.1016/S0550-3213(03)00048-8

We formulate the $O(3) \s-$ model on fuzzy sphere and construct the Hopf term. We show that the field can be expanded in terms of the ladder operators of Holstein-Primakoff realisation of SU(2) algebra and the corresponding basis set can be classified into different topological sectors by the magnetic quantum numbers. We obtain topological charge $Q$ and show that $-2j\le Q \le2j$. We also construct BPS solitons. Using the covariantly conserved current, we construct the Hopf term and show that its value is $Q^2$ as in the commutative case. We also point out the interesting relation of physical space to deformed SU(2) algebra.

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