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(2+1)D Noncommutative CP$^{N-1}$ Model

E. A. Asano·M. Gomes·A. G. Rodrigues·A. J. da Silva
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Abstract

We investigate possible extensions of the (2+1) dimensional $CP^{N-1}$ model to the noncommutative space. Up to the leading nontrivial order of 1/N, we prove that the model restricted to the left fundamental representation of the gauge group is renormalizable and does not have dangerous infrared divergences. In contrast, if the basic field $ϕ$ transforms in accord with the adjoint representation, infrared singularities are present in the two point function of the auxiliary gauge field and also in the leading correction to the self-energy of the $ϕ$ field. These infrared divergences may produce nonintegrable singularities leading at higher orders to a breakdown of the 1/N expansion. Gauge invariance of the renormalization procedure is also discussed.

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E. A. Asano, M. Gomes, A. G. Rodrigues, A. J. da Silva. 2003-12-02. (2+1)D Noncommutative CP$^{N-1}$ Model. https://doi.org/10.1103/physrevd.69.065012

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