Non-commutative duality: High spin fields and CP < sup > 1 < /sup > model with Hopf term

Abstract

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 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 → 0 giving dual theory in the commutative plane. © 2004 Elsevier B.V. All rights reserved.