Jordanian deformations of the AdS5 × S5 superstring

Kawaguchi, I.; Matsumoto, Takuya; Yoshida, Kentaroh

doi:10.1007/jhep04(2014)153

Cited by 217 publications

(364 citation statements)

References 57 publications

(98 reference statements)

Supporting

Mentioning

358

Contrasting

Unclassified

Order By: Relevance

“…Indeed, this is the case. As explained in detail in [53] , the r-matrix that leads to the Jordanian deformed solution [54] is constructed by performing a Jordanian twist of the r-matrix of Drinfeld-Jimbo type [45,46]. Hence this observation suggests that the Jordanian twist at the r-matrix level corresponds to the pp-wave like limit at the geometry level, as depicted in figure 1.…”

Section: A Possible Relation Between Gravitational Solutionsmentioning

confidence: 96%

“…This system is derived as a pp-wave like limit of the time-like warped SL(2) LLSM, as shown in detail in appendix D. The resulting system also coincides with a fast-moving string limit of Sch 3 ×S 1 subsector of the Jordanian deformed AdS 5 ×S 5 superstring action [53,54]. It is convenient to introduce a vector notation n a ,…”

Section: The Classical Action and Lax Pairmentioning

confidence: 99%

“…Jordanian deformed AdS 5 ×S 5 superstring actions have been constructed with linear R-operators satisfying classical Yang-Baxter equation [53]. A remarkable point is that partial deformations are possible in comparison to the standard q-deformation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

Kameyama

Yoshida

2014

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

Abstract:We consider bosonic subsectors of the q-deformed AdS 5 ×S 5 superstring action and study the classical integrable structure of anisotropic Landau-Lifshitz sigma models (LLSMs) derived by taking fast-moving string limits. The subsectors are 1) deformed AdS 3 × S 1 and 2) R × deformed S 3 . The cases 1) and 2) lead to a time-like warped SL(2) LLSM and a squashed S 3 LLSM, respectively. For each of them, we construct an infinite number of non-local conserved charges and show a quantum affine algebra at the classical level. Furthermore, a pp-wave like limit is applied for the case 1). The resulting system is a null-like warped SL(2) LLSM and exhibits a couple of Yangians through non-local gauge transformations associated with Jordanian twists.

show abstract

Section: A Possible Relation Between Gravitational Solutionsmentioning

confidence: 96%

Section: The Classical Action and Lax Pairmentioning

confidence: 99%

See 1 more Smart Citation

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

Kameyama

Yoshida

2014

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…A q-deformation with a classical r-matrix satisfying the mcybe has been studied in [36,37]. Jordanian deformations based on the cybe have been proposed in [38]. In the latter case, there are a lot of classical r-matrices satisfying the cybe and some of them are associated with well-known gravitational backgrounds, such as Lunin-Maldacena-Frolov backgrounds [39,40], gravity duals for non-commutative gauge theories [41,42], Schrödinger spacetimes [43][44][45][46][47] and gravity duals for dipole theories [48][49][50][51][52], as shown in a series of works [53][54][55][56][57].…”

Section: Jhep10(2015)185mentioning

confidence: 99%

Yang-Baxter deformations of Minkowski spacetime

Matsumoto

Orlando

Reffert

et al. 2015

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…In the presence of anomalies [7][8][9], this aspect of T-duality, including its generalizations [10][11][12][13], is obscured. In recent years, driven by developments in integrable deformations of σ-models [14][15][16][17], especially [18,19], we have started to understand these anomalies through a modification of supergravity, called "generalized supergravity" [20] (also [21]). The modification is encoded in an extra Killing vector I, with usual supergravity recovered when I ¼ 0.…”

Section: Introductionmentioning

confidence: 99%

Classical Yang-Baxter equation from supergravity

et al. 2018

View full text Add to dashboard Cite

We promote the open-closed string map, originally formulated by Seiberg & Witten, to a solution generating prescription in generalized supergravity. The approach hinges on a knowledge of an antisymmetric bivector Θ, built from antisymmetric products of Killing vectors, which is specified by the equations of motion. In the cases we study, the equations of motion reproduce the classical Yang-Baxter equation (CYBE) and Θ is the most general r-matrix solution. Our work generalizes Yang-Baxter deformations to non-coset spaces and unlocks gravity as a means to classify r-matrix solutions to the CYBE.

show abstract

Jordanian deformations of the AdS5 × S5 superstring

Cited by 217 publications

References 57 publications

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

Yang-Baxter deformations of Minkowski spacetime

Classical Yang-Baxter equation from supergravity

Contact Info

Product

Resources

About