Yang-Baxter σ-models and dS/AdS T-duality

Klimčı́k, Ctirad

doi:10.1088/1126-6708/2002/12/051

Cited by 357 publications

(720 citation statements)

References 23 publications

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“…The Poisson-Lie dual is then given by integrating out the degrees of freedom associated tok. Such configurations have been considered previously in [10,38,41]. Although given in a different form, which is of use in the application to the η deformation in section 3, the presented results are equivalent.…”

Section: Jhep11(2017)014mentioning

confidence: 96%

“…The matrices a, b and Π obey 10) with similar relations holding forã,b andΠ. In the absence of spectator fields, the sigma model whose background satisfies (2.4) and its dual are then given by…”

Section: Jhep11(2017)014mentioning

confidence: 99%

“…We start from the first-order action on the Drinfel'd double [10,37,38,41]. In the standard decomposition of the Drinfel'd double d = g +g, both g andg are Lie algebras.…”

Section: Jhep11(2017)014mentioning

confidence: 99%

“…Starting from the corresponding model on the Drinfel'd double (2.20) this allows us to investigate in which subgroups of G the η deformed model can be Poisson-Lie dualised and construct the corresponding backgrounds. Our starting point for the construction of the η deformed model will be the compact simple Lie group G, with Lie algebra g = Lie(G), and the complex Drinfel'd double D ≡ G C , with Lie algebra d ≡ g C = Lie(D) [10,12,33,41].…”

Section: The η and λ * Deformed Modelsmentioning

confidence: 99%

“…The η deformation of the AdS 5 ×S 5 superstring [1,2] generalises a certain integrable deformation of the principal chiral model [10,11] and of the symmetric space sigma model [12], often referred to as Yang-Baxter sigma models due to their explicit dependence on a nonsplit solution of the modified classical Yang-Baxter equation. The model depends on two parameters: an overall coupling h, which plays the role of the effective string tension, and the deformation parameter η.…”

Section: Introductionmentioning

confidence: 99%

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Poisson-Lie duals of the η deformed symmetric space sigma model

Hoare

Seibold

2017

J. High Energ. Phys.

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Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. In this paper we investigate when the η deformed model can be dualised with respect to a subgroup G 0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G 0 is associated to a subDynkin diagram. Additional U 1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the η deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the η deformed AdS 5 × S 5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the λ deformed model are.

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Section: Jhep11(2017)014mentioning

confidence: 96%

Section: Jhep11(2017)014mentioning

confidence: 99%

“…We start from the first-order action on the Drinfel'd double [10,37,38,41]. In the standard decomposition of the Drinfel'd double d = g +g, both g andg are Lie algebras.…”

Section: Jhep11(2017)014mentioning

confidence: 99%

Section: The η and λ * Deformed Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Poisson-Lie duals of the η deformed symmetric space sigma model

Hoare

Seibold

2017

J. High Energ. Phys.

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Generalised T‐duality and Integrable Deformations

Thompson

2015

Fortschritte der Physik

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Improvement of a Conserved Current Density Versus Adding a Total Derivative to a Lagrangian Density

Gieres

2022

Fortschritte der Physik

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For classical relativistic field theory in Minkowski space‐time, the addition of a superpotential term to a conserved current density is trivial in the sense that it does not modify the local conservation law nor change the conserved charge, though it may allow us to obtain a current density with some improved properties. The addition of a total derivative term to a Lagrangian density is also trivial in the sense that it does not modify the equations of motion of the theory. These facts suggest that both operations are related and possibly equivalent to each other for any global symmetry of an action functional. We address this question following the study of two quite different (and well known) instances: the Callan‐Coleman‐Jackiw improvement of the canonical energy‐momentum tensor for scalar and vector fields (providing an on‐shell traceless energy‐momentum tensor) and the construction of a current density satisfying a zero curvature condition for two‐dimensional sigma models on deformed spaces (notably the squashed three‐sphere and warped AdS spaces). These instances correspond to fairly different implementations of the general results. An appendix addresses the precise relationship between the approaches to local conservation laws based on active and passive symmetry transformations, respectively.

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Yang-Baxter σ-models and dS/AdS T-duality

Cited by 357 publications

References 23 publications

Poisson-Lie duals of the η deformed symmetric space sigma model

Poisson-Lie duals of the η deformed symmetric space sigma model

Generalised T‐duality and Integrable Deformations

Improvement of a Conserved Current Density Versus Adding a Total Derivative to a Lagrangian Density

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