On the energy crisis in noncommutative CP(1) model

Details On the energy crisis in noncommutative CP(1) model On the energy crisis in noncommutative CP(1) model

2010-01-27

arxiv.org/abs/1001.5064v5

Nucl.Phys.B834:471-484,2010

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, minor corrections

Scientific paper

10.1016/j.nuclphysb.2010.03.005

We study the CP(1) system in (2+1)-dimensional noncommutative space with and without Chern-Simons term. Using the Seiberg-Witten map we convert the noncommutative CP(1) system to an action written in terms of the commutative fields. We find that this system presents the same infinite size instanton solution as the commutative Chern-Simons-CP(1) model without a potential term. Based on this result we argue that the BPS equations are compatible with the full variational equations of motion, rejecting the hypothesis of an "energy crisis". In addition we examine the noncommutative CP(1) system with a Chern-Simons interaction. In this case we find that when the theory is transformed by the Seiberg-Witten map it also presents the same instanton solution as the commutative Chern-Simons-CP(1) model.

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