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

T. R. Govindarajan·E. Harikumar
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Abstract

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 $θ$ and show that the spin of the dual theory do not get any $θ$ dependant corrections. The map between current correlators show that topological index of the solitons in the non-commutative $CP^1$ model is unaffected by $θ$ where as the Noether charge of the corresponding dual particle do get a $θ$ dependence. We also show that this dual theory smoothly goes to the limit $θ\to 0$ giving dual theory in the commutative plane.

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BibTeXRIS

T. R. Govindarajan, E. Harikumar. 2004-10-19. Non-commutative Duality: High Spin Fields and $CP^1$ Model with Hopf Term. https://doi.org/10.1016/j.physletb.2004.09.070

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