Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable σ-model

Delduc, F.; Hoare, Ben; Kameyama, Takashi; Magro, Marc

doi:10.1007/jhep10(2017)212

Cited by 45 publications

(65 citation statements)

References 48 publications

(111 reference statements)

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“…As explained in Subsection 4.1.3, this is already an interesting question for models with only one copy, which correspond to multi-parameter deformations of the Principal Chiral Model (or its non-abelian T-dual). It would be for example desirable to compare the models obtained this way with some of the multi-parameter deformations already existing in the literature, such as the generalised λ-deformed model introduced in [29] and the 3-parameter model constructed in [27]. These models have been shown to possess a Lax pair formulation at the Lagrangian level ; however, their Hamiltonian analysis and the study of the Poisson bracket of their Lax matrix has not been per-formed yet.…”

Section: Resultsmentioning

confidence: 99%

Constrained affine Gaudin models and diagonal Yang–Baxter deformations

Lacroix¹

2020

J. Phys. A: Math. Theor.

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We review and pursue further the study of constrained realisations of affine Gaudin models, which form a large class of two-dimensional integrable field theories with gauge symmetries. In particular, we develop a systematic gauging procedure which allows to reformulate the non-constrained realisations of affine Gaudin models considered recently in [1] as equivalent models with a gauge symmetry. This reformulation is then used to construct integrable deformations of these models breaking their diagonal symmetry. In a second time, we apply these general methods to the integrable coupled σ-model introduced recently, whose target space is the N -fold Cartesian product G N 0 of a real semi-simple Lie group G 0 . We present its gauged formulation as a model on G N +1 0 with a gauge symmetry acting as the right multiplication by the diagonal subgroup G diag 0 and construct its diagonal homogeneous Yang-Baxter deformation.

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Section: Resultsmentioning

confidence: 99%

Constrained affine Gaudin models and diagonal Yang–Baxter deformations

Lacroix¹

2020

J. Phys. A: Math. Theor.

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“…Further, both these deformations can be combined together, along with ones of the class c = 0, and on a suitable locus of coupling parameters they give an integrable model whose Lax was explicitly realised in [167].…”

Section: Multi-parameter η-Deformationsmentioning

confidence: 99%

An Introduction to Generalised Dualities and their Applications to Holography and Integrability

Thompson¹

2019

Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018)

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These pedagogical lectures given at the Corfu Summer Institute 2018 review two generalised notions of T-duality, non-Abelian T-duality and Poisson-Lie duality, and their applications. We explain how each of these has seen recent application in the context of holography. Non-Abelian T-duality has been used to construct new holographic dual geometries. Poisson-Lie duality has been used to construct new integrable string sigma-models including the η-and λ -deformations of the AdS 5 × S 5 superstring thought to encode quantum group deformations of holography. We also comment on the doubled worldsheet description that makes such dualities manifest. duality serves to interchange a conservation law, that associated to the U(1) global symmetry of the compact boson θ of radius R, with the Bianchi identity for the dual bosonθ :( 1.3) Just as with bosonisation the connection between the two variables involves derivatives, i.e. the map between variables is a non-local one. Also akin to the Abelian bosonisation, the dual theory can be established through an analogous path integral manipulation 1 known as the Buscher procedure [22,23]. Given the close analogy between T-duality and Abelian bosonisation one might wonder if there is a T-duality equivalent to non-Abelian bosonisation. More specifically, in string theory we are immediately prompted to ask if there is an extension of T-duality to the case of a non-Abelian set of isometries, or even if there are still more exotic notions of T-duality? A secondary question is then, if such dualities exist, what are they useful for? The remainder of these lectures seek to outline some answers to these two questions.Our journey will involve exploring a hierarchy of possible dualities in the following string theory scenarios:

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“…With an R-matrix solving (2.2) at hand, let us introduce the following deformation of the PCM known as the Yang-Baxter Wess-Zumino model [9],…”

Section: )mentioning

confidence: 99%

“…Indeed it has proven to be critical in the providing explicit examples of generalised T-dualities [5,6] and understanding the role of quantum groups in integrable systems [7,8]. Both these aspects will be discussed in this talk for the particular case of an integrable deformation called the Yang-Baxter Wess-Zumino (YB-WZ) model [9]. The YB-WZ model is integrable as its equation of motion can be put into a Lax form.…”

Section: Introductionmentioning

confidence: 99%

Quantum properties and generalised T-duality of the Yang-Baxter Wess-Zumino model

Demulder

2019

Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018)

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In this short proceedings we discuss some of the results obtained in [1]. Integrable deformations enlarge the landscape and understanding of integrable models and its algebraic structures like quantum groups. In this short proceedings, we will review the one-loop renormalisation group analysis of an integrable deformation known as the Yang-Baxter Wess-Zumino model. This classically integrable model shows a striking stability under one-loop renormalisation. In addition, we show how Poisson-Lie T-duality, a generalisation of T-duality that is closely intertwined with integrable deformations, is particularly simple and elegant for the Yang-Baxter Wess-Zumino model.

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Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable σ-model

Cited by 45 publications

References 48 publications

Constrained affine Gaudin models and diagonal Yang–Baxter deformations

Constrained affine Gaudin models and diagonal Yang–Baxter deformations

An Introduction to Generalised Dualities and their Applications to Holography and Integrability

Quantum properties and generalised T-duality of the Yang-Baxter Wess-Zumino model

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