2013/05/31 by Io Kawaguchi, Takuya Matsumoto, Kentaroh Yoshida
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Gauge (firearms) #Gauge symmetry #Gauge theory #Geometry #Integrable system #Isotropy #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum mechanics #Realization (probability) #Sigma #Sigma model #Symmetry (geometry) #Twist #Yangian #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1007/jhep08(2013)013
40 pages, 2 figures, LaTeX, typos corrected, references added, further clarification
arxiv created 2013/06/06 · openalex publication_date 2013/08/01 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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)).