Hybrid classical integrability in squashed sigma models

Details Hybrid classical integrability in squashed sigma models Hybrid classical integrability in squashed sigma models

2011-07-19

arxiv.org/abs/1107.3662v2

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX, typos corrected and references added, to appear in PLB

Scientific paper

We show that SU(2)_L Yangian and q-deformed SU(2)_R symmetries are realized in a two-dimensional sigma model defined on a three-dimensional squashed sphere. These symmetries enable us to develop the two descriptions to describe its classical dynamics, 1) rational and 2) trigonometric descriptions. The former 1) is based on the SU(2)_L symmetry and the latter 2) comes from the broken SU(2)_R symmetry. Each of the Lax pairs constructed in both ways leads to the same equations of motion. The two descriptions are related one another through a non-local map.

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