Comment on ”non-commutative Duality: High Spin Fields and Cp (1) Model with Hopf Term”

We comment on a recent paper (hep-th/0406273) [1] where Non-Commutative (NC) extension of the CP (1) model coupled to Hopf term and its equivalence with an interacting spin system has been considered. We argue that the NC CP (1) model with Hopf term, along with the constraint structure, as formulated in [1] is incomplete. However, the final results obtained in [1] can be made consistent after a proper interpretation of the model. Results previously obtained in [2] play crucial roles in the analysis. ——————————————— In a recent paper, Govindarajan and Harikumar [1] have discussed a duality concerning CP (1) model coupled to the Hopf term and an interacting spin s theory in the NonCommutative (NC) plane. The very same model (NC CP (1) without the Hopf term) has been studied in detail in [2], where problems related to the inclusion of the Hopf term in the present setup was also commented upon. Referring to our results in [2], we find that in the analysis of the NC extension of the CP (1)-Hopf model [1], the authors have imposed an incomplete set of constraints, which makes the constrained path integral considered by them incorrect. We also discuss a new interpretation of the NC CP (1)-Hopf model in which the results obtained in [1] are plausible. Once again results and conclusions of [2] play a vital role. As is well-known, in the CP (1) model in ordinary spacetime, one starts with the gauge