Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term

Abstract

We show that the non-commutative $C{P}^1$ model coupled with Hopf term in 3 dimensions is equivalent to an interacting spin-$s$ theory where the spin $s$ of the dual theory is related to the coefficient of the Hopf term. We use the Seiberg-Witten map in studying this non-commutative duality equivalence, keeping terms to order $\theta$ and show that the spin of the dual theory do not get any $\theta$ dependant corrections. The map between current correlators show that topological index of the solitons in the non-commutative $C{P}^1$ model is unaffected by $\theta$ where as the Noether charge of the corresponding dual particle do get a $\theta$ dependence. We also show that this dual theory smoothly goes to the limit $\theta \to 0$ giving dual theory in the commutative plane.

13 pages, more references and a footnote are added. Version to appear in Phys. Lett. B

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Cited by in corpus (6)

• Topics in Noncommutative Geometry Inspired Physics
• Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual
• The Supersymmetric (2+1)D Noncommutative $C{P}^{(N-1)}$ Model in the Fundamental Representation
• Aspects of Noncommutative Scalar/Tensor Duality
• Topological stability of broken symmetry on fuzzy spheres
• Bose-Fermi Equivalence in Three Dimensional Non-commutative Space-Time