Hybrid classical integrability in squashed sigma models

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.

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

References in corpus (8)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Charged Magnetic Brane Solutions in AdS_5 and the fate of the third law of thermodynamics
• Strings on Semisymmetric Superspaces
• Yangian symmetry in deformed WZNW models on squashed spheres
• Holographic Metamagnetism, Quantum Criticality, and Crossover Behavior
• Hidden Yangian symmetry in sigma model on squashed sphere
• Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality

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