Hybrid classical integrability in squashed sigma models

2011/07/31 by Io Kawaguchi, Kentaroh Yoshida · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/j.physletb.2011.09.117

12 pages, LaTeX, typos corrected and references added, further clarification added

arxiv created 2012/11/13 · arxiv updated 2015/05/28

Abstract

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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