S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models

Jun 22, 2015
25 pages
Published in:
  • J.Phys.A 49 (2016) 46, 465201
  • Published: Oct 21, 2016
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Abstract: (IOP)
Recently, two kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed (Delduc et al 2014 Phys. Rev. Lett. 112 051601, Hollowood et al 2014 J. Phys. A: Math. Theor. 47 495402). One class of these, the k deformations associated to the more general q deformations but with q=eiπ/kq={{\rm{e}}}^{{\rm{i}}\pi /k} a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
Note:
  • 32 pages, added reference, changed nomenclature from q deformed to k deformed to distinguish from eta deformation
  • deformation: discrete
  • field theory: integrability
  • model: chiral
  • quantum group
  • S-matrix
  • sigma model
  • Wess-Zumino-Witten model
  • gravitation
  • scattering
  • string