Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality

Abstract

We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti-de Sitter space and the Schroedinger spacetime. These models can be obtained via T-duality from integrable models. We construct an infinite family of non-local conserved charges from the T-dual Lax currents, enhancing the symmetry of warped anti-de Sitter space and the Schroedinger spacetime to sl2(R)+sl2(R).

29 Pages, 3 appendices. Minor changes: added references, footnote

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• Non-integrability in non-relativistic theories
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• The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation
• Affine q-deformed symmetry and the classical Yang-Baxter sigma-model
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Integrable Superstrings on the Squashed Three-sphere
• Lifshitz-like systems and AdS null deformations
• Semiclassical spectrum for BMN string in $Sc{h}_5\times S^5$
• Yang-Baxter deformations and generalized supergravity -- A short summary
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• Yang-Baxter deformations of Minkowski spacetime
• An Index for Quantum Integrability
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
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