On classical q-deformations of integrable σ-models
By F. Delduc, Marco Magro, B. Vicedo. 2013
245 citations recorded by the source corpus.
A bstractA 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.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ad64897fffc8933e872aab66bdc40c50f3fb24b0
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Integrable deformations of strings on symmetric spaces (2014, background): “Importantly, the deformation considered in [14] corresponds to 2 ≥ 0 and it turns out to be defined only for 0 ≤ 2 < 1; i.”
- An integrable deformation of the AdS5 × S5 superstring (2014, background): “At the classical level the deformed theories have the same equations of motion but different symplectic structures [11, 12, 15].”
- Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence (2014, result): “Though it was originally argued for principal chiral models, Delduc, Magro and Vicedo succeeded to generalize it to symmetric coset cases [35], where the standard q-deformed algebra is presented as a generalization of [27, 28].”
- On integrable deformations of superstring sigma models related to AdSn×Sn supercosets (2015, background): “, together with expected quantum UV niteness, suggest that classical relations may in some way extend to the quantum level. 6For both deformed models, there was a paper focussing on the bosonic case, [4] and [5], written before the papers discussing the deformation of the superstring, [1] and [6] re”
- Abelian Yang–Baxter deformations and TsT transformations (2016, methodology): “This notion was generalised to symmetric space coset σ models in [10] and then further to the supercoset σ model describing the AdS5 × S5 superstring [11].”
- Target space supergeometry of η and λ-deformed strings (2016, background): “The η-model [5] and λ-model [6], named after the corresponding deformation parameters. The former is based on the Yang-Baxter deformation of [7, 8, 9], it generalises the case of bosonic coset models [10], and its essential ingredient is an R-matrix which satisfies the modified classical Yang-Baxter e”
- Jordanian deformations of the AdS5 × S5 superstring (2014, methodology): “In particular, the method utilized in [36] is based on Yang-Baxter sigma models [37, 38].”
- Generalised integrable λ- and η-deformations and their relation (2015, methodology): “[h, h] ⊆ h, [h, k] ⊆ k and [k, k] ⊆ h) has already been considered in the literature – an integrable YB σ -model is given by [4]”
- Integrability of the Bi-Yang–Baxter σ-Model (2014, methodology): “ss some limiting cases of the parameters α and β and, as a by-product of this discussion, we establish the gauge equivalence of the Lax pairs of the simple Yang-Baxter σ-model obtained in [14] and in [4], respectively. In Section 3, we discuss the notion of the extended solution of the Yang-Baxter σ”
- Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory (2015, result): “1 This generalizes the earlier results of [8–10].”
- Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles (2015, methodology): “Sometimes these are also referred to as q-deformations since the global symmetry algebra of these theories was shown to be q-deformed [4] with q a function of”