Non-commutative duality: high spin fields and [formula omitted] 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 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.