Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-04-23
Phys.Rev.D78:065020,2008
Physics
High Energy Physics
High Energy Physics - Theory
17+1 pages, LaTeX, Added references, corrected typos, published version
Scientific paper
10.1103/PhysRevD.78.065020
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_\theta(R^2+1). By extending a generalized zero curvature representation to A_\theta(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_\theta(R^1+1|2), A_\theta(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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