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Non-commutative duality: high spin fields and CP1 model with Hopf term

Physics Letters B, ISSN: 0370-2693, Vol: 602, Issue: 3, Page: 238-248
2004
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We show that the non-commutative CP1 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 shows that topological index of the solitons in the non-commutative CP1 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→0 giving dual theory in the commutative plane.

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