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

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, keep...

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Bibliographic Details
Published in:Physics letters. B 2004-11, Vol.602 (3-4), p.238-248
Main Authors: Govindarajan, T.R., Harikumar, E.
Format: Article
Language:English
Subjects:
Duality
Exact sciences and technology
Field theory
General theory of fields and particles
High spin fields
Non-commutative plane
Physics
The physics of elementary particles and fields
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Summary: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.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2004.09.070