Yangian symmetry in deformed WZNW models on squashed spheres

Yoshida

2012

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We consider a quantum affine algebra realized in two-dimensional nonlinear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassical limit of quantum affine algebra at quantum level.

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Although the squashed sigma models are well known as an integrable model of the trigonometric class, it has been shown that a Yangian symmetry Y (sl (2)) is realized even after the squashing in a series of works [22][23][24] (For a short summary see [25]). This result may sound curious.…”

Section: Introductionmentioning

confidence: 99%

The classical origin of quantum affine algebra in squashed sigma models

Kawaguchi

Yoshida

2012

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“…Although deformed target spaces are not represented by symmetric cosets 2 and there is no general prescription to argue the integrability, many techniques have been developed and various aspects have been revealed. Especially for squashed S 3 , the Lax pair was presented in [22] and the classical integrable structure has been elaborated in the subsequent works [23][24][25][26][27][28][29][30][31][32][33][34]. As a possible way toward higher-dimensional cases, the Yang-Baxter sigma model approach was proposed by Klimcik [17][18][19].…”

Section: Jhep06(2014)135mentioning

confidence: 99%

Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence

Yoshida

2014

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107

175

Abstract:We consider γ-deformations of the AdS 5 ×S 5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real γ-deformations of the AdS 5 ×S 5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.

“…Deformations of S 3 and AdS 3 have been well investigated [8][9][10][11][12][13][14][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. 1 A systematic way is the Yang-Baxter sigma model approach proposed by Klimcik [11][12][13].…”

Section: Jhep10(2015)185mentioning

confidence: 99%

Yang-Baxter deformations of Minkowski spacetime

Orlando

Reffert

et al. 2015

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We study Yang-Baxter deformations of 4D Minkowski spacetime. The YangBaxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS 5 by embedding the 4D Poincaré group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS 4 and AdS 4 . Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.