Non-commutative Duality: High Spin Fields and $CP^1$ Model with Hopf Term

Details Non-commutative Duality: High Spin Fields and $CP^1$ Model with Hopf Term Non-commutative Duality: High Spin Fields and $CP^1$ Model with Hopf Term

2004-06-30

arxiv.org/abs/hep-th/0406273v3

Phys.Lett. B602 (2004) 238-248

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/j.physletb.2004.09.070

We show that the non-commutative $CP^1$ 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 $CP^1$ 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.

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