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

Abstract

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 $-2j\le Q\le 2j$. 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.

arXiv comment17 pages, Latex, typos corrected, added one reference, to appear in Nucl. Phys. B Reprt-no: IMSc/2002/11/39

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Cited by in corpus (8)

• Scalar Field Theory on Fuzzy S^4
• Non-Linear Sigma Model on the Fuzzy Supersphere
• Dirac operator on the q-deformed Fuzzy sphere and Its spectrum
• Fuzzy Nambu-Goldstone Physics
• Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term
• 'Schwinger Model' on the Fuzzy Sphere
• Nonlocal regularisation of noncommutative field theories
• Duality in Fuzzy Sigma Models