On classical qq-deformations of integrable sigma-models

Aug 16, 2013
37 pages
Published in:
  • JHEP 11 (2013) 192
  • Published: 2013
e-Print:

Citations per year

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Abstract: (arXiv)
A procedure is developed for constructing deformations of integrable sigma-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter sigma-model introduced a few years ago by C. Klimcik. In the case of the symmetric space sigma-model on F/G we obtain a new one-parameter family of integrable sigma-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset sigma-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset sigma-model which interpolates all the way to the SU(1,1)/U(1) coset sigma-model.
Note:
  • 38 pages, 1 figure
  • Integrable Field Theories
  • Sigma Models
  • Quantum Groups
  • model: chiral
  • group: Lie
  • sigma model
  • integrability
  • deformation
  • Yang-Baxter
  • geometry