O(3) sigma model with Hopf term on fuzzy sphere

Abstract

We formulate the O(3) σ-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 ≤ Q ≤ 2j. We also construct BPS solitons. Using the covariantly conserved current, we construct the Hopf term and show that its value is Q2 as in the commutative case. We also point out the interesting relation of physical space to deformed SU(2) algebra. © 2003 Elsevier Science B.V. All rights reserved.