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arXiv · 0804.3782

Noncommutative Nonlinear Sigma Models and Integrability

Seckin Kurkcuoglu
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Abstract

We first review the result that the noncommutative principal chiral model has an infinite tower of conserved currents, and discuss the special case of the noncommutative CP^1 model in some detail. Next, we focus our attention to a submodel of the CP^1 model in the noncommutative spacetime A_θ(R^2+1). By extending a generalized zero curvature representation to A_θ(R^2+1) we discuss its integrability and construct its infinitely many conserved currents. Supersymmetric principal chiral model with and without the WZW term and a supersymmetric extension of the CP^1 submodel in noncommutative spacetime (i.e in superspaces A_θ(R^1+1|2), A_θ(R^2+1|2)) are also examined in detail and their infinitely many conserved currents are given in a systematic manner. Finally, we discuss the solutions of the aforementioned submodels with or without supersymmetry.

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Seckin Kurkcuoglu. 2008-09-15. Noncommutative Nonlinear Sigma Models and Integrability. https://doi.org/10.1103/physrevd.78.065020

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