Non Commutative Field Theories and Integrable Models in 2d

Details Non Commutative Field Theories and Integrable Models in 2d Non Commutative Field Theories and Integrable Models in 2d

2003-03-19

arxiv.org/abs/hep-th/0303168v1

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, 1 figure, talk given at the Workshop on Integrable Theories, Solitons and Dualities, IFT Sao Paulo, July 2002

Scientific paper

We study the noncommutative extensions of certain integrable field theories, namely the sine- and sinh-Gordon (sG and shG) models, and the U(N) principal chiral model (pcm). We argue that the Moyal deformations of the sG and shG models are not integrable, by looking at tree-level amplitudes where there is particle production. By considering the noncommutative generalization of the zero-curvature method, it is possible to define integrable versions of the noncommutative sG and shG models, which introduce extra constraints. The noncommutative pcm is shown to be integrable and we discuss the existence of non-trivial non-local conserved charges, and the associated noncommutative zero-curvature condition.

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