Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry
Sep, 2011Citations per year
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Abstract: (arXiv)
We discuss classical integrable structure of two-dimensional sigma models which have three-dimensional Schrodinger spacetimes as target spaces. The Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R due to the deformation. According to this symmetry, there are two descriptions to describe the classical dynamics of the system, 1) the SL(2,R)_L description and 2) the enhanced U(1)_R description. In the former 1), we show that the Yangian symmetry is realized by improving the SL(2,R)_L Noether current. Then a Lax pair is constructed with the improved current and the classical integrability is shown by deriving the r/s-matrix algebra. In the latter 2), we find a non-local current by using a scaling limit of warped AdS_3 and that it enhances U(1)_R to a q-deformed Poincare algebra. Then another Lax pair is presented and the corresponding r/s-matrices are also computed. The two descriptions are equivalent via a non-local map.Note:
- 20 pages, no figure, further clarification and references added
- current: nonlocal
- current: Noether
- pair: Lax
- symmetry: Yangian
- symmetry: Poincare
- space-time: Schroedinger
- deformation
- integrability
- sigma model
- field theory: conformal
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