Hybrid classical integrable structure of squashed sigma models -- a short summary

Details Hybrid classical integrable structure of squashed sigma models -- a short summary Hybrid classical integrable structure of squashed sigma models -- a short summary

2011-10-31

arxiv.org/abs/1110.6748v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Proceedings of QTS7, Prague, Czech Republic, 2011

Scientific paper

We give a short summary of our recent works on the classical integrable structure of two-dimensional non-linear sigma models defined on squashed three-dimensional spheres. There are two descriptions to describe the classical dynamics, 1) the rational description and 2) the trigonometric description. It is possible to construct two different types of Lax pairs depending on the descriptions, and the classical integrability is shown by computing classical r/s-matrices satisfying the extended Yang-Baxter equation in both descriptions. In the former the system is described as an integrable system of rational type. On the other hand, in the latter it is described as trigonometric type. There exists a non-local map between the two descriptions and those are equivalent. This is a non-local generalization of the left-right duality in principal chiral models.

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