Journal of High Energy Physics· 2013Q2
On classical q-deformations of integrable σ-models
- 327citations
- Q2SCImago
- 2013year
Short summary
A new method constructs classically integrable q-deformed σ-models, yielding a one-parameter family of models for symmetric spaces with a torsion term and q-deformed symmetries.
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Key points
- Developed a general procedure for constructing classically integrable q-deformations of integrable σ-models.
- The deformation of symmetric space σ-models yields a one-parameter family of integrable models with a torsion term.
- The left multiplication symmetry is replaced by a classical q-deformed Poisson-Hopf algebra.
- The deformation interpolates between compact and non-compact symmetric spaces, exemplified by SU(2)/U(1) and SU(1,1)/U(1) coset models.
AI-generated from the title and abstract; the full text is not read.
Abstract
A bstract A procedure is developed for constructing deformations of integrable σ -models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F , one recovers the Yang-Baxter σ -model introduced a few years ago by C. Klimčík. In the case of the symmetric space σ -model on F/G we obtain a new one-parameter family of integrable σ -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 σ -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 σ -model which interpolates all the way to the SU(1 , 1) / U(1) coset σ -model.
The authors' abstract, as published at the source. Journal of High Energy Physics, 2013 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics