Schrodinger Sigma Models and Jordanian Twists

Abstract

We proceed to study the integrable structures of two-dimensional non-linear sigma models defined on three-dimensional Schrodinger spacetimes. We show that anisotropic Lax pairs are equivalent with isotropic Lax pairs with flat conserved currents under non-local gauge transformations. Then a quite non-trivial realization of the undeformed Yangian symmetry Y(sl(2)) is revealed after an appropriate gauge fixing, which is determined by comparing the gauge transformation to a quantum Jordanian twist. As a result, an exotic symmetry found in arXiv:1209.4147 may be interpreted as a Jordanian deformation of Y(sl(2)).

40 pages, 2 figures, LaTeX, typos corrected, references added, further clarification

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• A Jordanian deformation of AdS space in type IIB supergravity
• Schrödinger geometries arising from Yang-Baxter deformations
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Non-integrability in non-relativistic theories
• A deformation of quantum affine algebra in squashed WZNW models
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• Comments on 2D dilaton gravity system with a hyperbolic dilaton potential
• Deformations of the Almheiri-Polchinski model
• Unimodular jordanian deformations of integrable superstrings
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• Supercoset construction of Yang-Baxter deformed AdS${}_5\times$S${}^5$ backgrounds
• Massless sector of AdS_3 superstrings: a geometric interpretation
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• $O(d,d)$ transformations preserve classical integrability
• Minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with Poincare coordinates
• Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$
• Yang-Baxter deformations of Minkowski spacetime
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• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
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• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background
• Geometry of Massless Scattering in Integrable Superstring
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Yang-Baxter deformations and string dualities