Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles

By B. Vicedo. 2015

171 citations recorded by the source corpus.

We describe a unifying framework for the systematic construction of integrable deformations of integrable σ-models within the Hamiltonian formalism. It applies equally to both the ‘Yang–Baxter’ type as well as ‘gauged WZW’ type deformations which were considered recently in the literature. As a byproduct, these two families of integrable deformations are shown to be Poisson–Lie T-dual of one another.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0c5ea3b9a0b8687f15bbdc7a80a1834b357cb32a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. S. J. Tongeren
2. B. Hoare
3. G. Arutyunov
4. R. Roiban
5. S. Frolov
6. David Osten
7. L. Wulff
8. R. Borsato

In Geometry and Topology

1. G. Arutyunov
2. S. Frolov
3. A. Tseytlin
4. S. J. Tongeren
5. R. Borsato
6. R. Roiban
7. L. Wulff
8. David Osten

In Statistical and Nonlinear Physics

1. S. Frolov
2. A. Tseytlin
3. G. Arutyunov
4. R. Roiban
5. R. Borsato
6. S. J. Tongeren
7. David Osten
8. B. Hoare

Citations in the corpus

• Target space supergeometry of η and λ-deformed strings (2016, background): “l symmetry algebra gets q-deformed [14, 15] (with qreal and root of unity respectively), and the two models are related, at least at the classical level, by the Poisson-Lie T-duality of [16, 17], see [18, 19, 20]. The attempt of interpreting these deformations as string theories has raised interesti”
• Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations (2015, background): “26 Thus if the classical Poisson-Lie duality relation [25] between the η -model and λ -model [26, 12] extends to the full quantum level there may be a way to associate a string theory to the ABF background.”
• On integrable deformations of superstring sigma models related to AdSn×Sn supercosets (2015, methodology): “[37] giving a general Hamiltonian construction of the relation of the two deformed models via the Poisson-Lie duality complementing our discussion in section 5.”
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory (2015, background): “to dS 5 ×H5 [7,11,14–16]. Also, interesting links to the λ-deformation of the non-abelian T dual of the AdS 5 ×S5 string [17–19], which have supergravity embeddings [20], have recently been uncovered [21,22]. These λ-deformations generalize the earlier work of [23]. 3TsT transformations are also kno”
• Abelian Yang–Baxter deformations and TsT transformations (2016, methodology): “9], guaranteeing scale but not Weyl invariance. 1 These models are related to another type of integrable deformation known as the λ model [12, 13, 14] by analytic continuation and Poisson-Lie duality [15, 16, 17, 18, 19, 20], see also [21]. The λ-type models do correspond to solutions of supergravit”