Yang-Baxter $\sigma$-models and dS/AdS T-duality

By C. Klimčík. 2002

342 citations recorded by the source corpus.

We point out the existence of nonlinear $\sigma$-models on group manifolds which are left symmetric and right Poisson-Lie symmetric. We discuss the corresponding rich T-duality story with particular emphasis on two examples: the anisotropic principal chiral model and the $SL(2,C)/SU(2)$ WZW model. The latter has the de Sitter space as its (conformal) non-Abelian dual.

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

View Paper: https://www.semanticscholar.org/paper/0cc6911b75860a0f7c940f48769b8beb79c27038

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In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

On integrable deformations of superstring sigma models related to AdSn×Sn supercosets (2015, neutral): “The first “η-model” is defined by the deformed supercoset action of [1] (generalizing the bosonic model of [2])(2) Îh,η(g) = h 2 ∫ d(2)x STr [ g∂+g Pη 1 1− 2η 1−η2RgPη g∂−g ] , (2.”
Integrability of the Bi-Yang–Baxter σ-Model (2014, methodology): “This is the case for specific metric deformations of principal chiral model on the SU (2) group [3,9,10] and on the Nappi–Witten group [19], respectively, for the Yang–Baxter σ -model on every simple compact group [16,17] and, finally, for the model interpolating between exact WZNW CFT and non-Abeli”
On classical q-deformations of integrable σ-models (2013, methodology): “This corresponds to the Yang-Baxter σ-model defined by Klimč́ık in [4,5].”
Jordanian deformations of the AdS5 × S5 superstring (2014, neutral): “In particular, the method utilized in [29] is based on Yang-Baxter sigma models [30].”
S-matrix for strings on η-deformed AdS5 × S5 (2013, background): “This class is not solely restricted to the string model in question but can be applied to a large variety of two-dimensional integrable models based on (super)groups or their cosets [17]-[20].”
Abelian Yang–Baxter deformations and TsT transformations (2016, methodology): “Yang-Baxter σ models were introduced as deformations of principal chiral models based on R operators solving the modified classical Yang-Baxter equation [8], preserving their integrability [9].”
Integrable deformations of strings on symmetric spaces (2014, methodology): “This kind of deformed sigma-model is a generalization of the so-called Yang-Baxter deformation introduced by Klimč́ık [19].”
Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles (2015, background): “The first family of integrable deformations was originally introduced by Klimč́ık in the case of the principal chiral model on an arbitrary (compact) real Lie group G [1, 2].”
Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence (2014, methodology): “As a possible way toward higher-dimensional cases, the Yang-Baxter sigma model approach was proposed by Klimcik [17–19].”
Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations (2015, methodology): “Just from the construction of this “η-model” (based on a particular current–current deformation of the supercoset action [2] generalising the bosonic model of [3]) there is no a priori reason why it should define a scale invariant (UV finite) 2d theory and, moreover, why it should preserve the confo”