Lax pairs for deformed Minkowski spacetimes

Kyono, Hideki; Sakamoto, Jun; Yoshida, Kentaroh

doi:10.1007/jhep01(2016)143

Cited by 10 publications

(14 citation statements)

References 84 publications

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“…In fact, the background (4.20) satisfies the generalized type IIB supergravity equations of motion proposed in [19]. Detailed analysis will be presented in a future paper [39].…”

Section: A Non-abelian Classical R-matrixmentioning

confidence: 86%

Supercoset construction of Yang–Baxter-deformed AdS5×S5 backgrounds

Kyono

Yoshida

2016

Prog. Theor. Exp. Phys.

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117

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We proceed to study Yang-Baxter deformations of the AdS 5 ×S 5 superstring with the classical Yang-Baxter equation. We make a general argument on the supercoset construction and present a formula to describe the dilaton in terms of classical rmatrices. The supercoset construction is explicitly performed for some classical rmatrices and the full backgrounds including the Ramond-Ramond (R-R) sector and dilaton are derived. Within the class of abelian r-matrices, the perfect agreement is shown for well-known examples including gravity duals of non-commutative gauge theories, γ-deformations of S 5 and Schrödinger spacetimes. It is remarkable that the supercoset construction works well, even if the resulting backgrounds are not maximally supersymmetric. In particular, three-parameter γ-deformations of S 5 and Schrödinger spacetimes do not preserve any supersymmetries. As for non-abelian r-matrices, we will focus upon a specific example. The resulting background does not satisfy the equation of motion of the Neveu-Schwarz-Neveu-Schwarz (NS-NS) two-form becauseThis coset enjoys the Z 4 -grading property and ensures classical integrability [9] (for a nice review, see [10]). The integrability plays an important role in checking the conjectured relation in AdS/CFT (for a comprehensive review, see [11]). By employing the Yang-Baxter deformation, Delduc, Magro and Vicedo constructed the classical action of a q-deformed AdS 5 ×S 5 superstring [12]. This deformation comes from the classical r-matrix of Drinfel'd-Jimbo type satisfying the mCYBE [13]. The string-frame metric and Neveu-Schwarz-Neveu-Schwarz (NS-NS) two-form were derived by Arutyunov, Borsato and Frolov [14]. Then they performed the supercoset construction and derived the remaining sector [15] (for earlier attempts, see [16, 17]). As a result, the full background does not satisfy the equations of motion of type IIB supergravity, although it is related to a complete solution [18] via T-dualities apart from the dilaton part. In particular, the dilaton cannot be separated so that the Ramond-Ramond (R-R) flux should satisfy the Bianchi identity. Recently, Arutyunov et al. proposed an exciting conjecture that type IIB supergravity itself would get deformed, for example, the definition of R-R field strength may be modified [19]. This "modified gravity conjecture" may be connected to our result presented here.One may also consider Yang-Baxter deformations of the AdS 5 ×S 5 superstring with classical r-matrices satisfying the homogeneous CYBE [20]. A strong advantage in this case is that partial deformations of AdS 5 ×S 5 are possible. In fact, for well-known backgrounds including gravity duals of noncommutative gauge theories [21,22], γ-deformations of S 5 [23,24],

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“…In fact, the background (4.20) satisfies the generalized type IIB supergravity equations of motion proposed in [19]. Detailed analysis will be presented in a future paper [39].…”

Section: A Non-abelian Classical R-matrixmentioning

confidence: 86%

Supercoset construction of Yang–Baxter-deformed AdS5×S5 backgrounds

Kyono

Yoshida

2016

Prog. Theor. Exp. Phys.

Self Cite

117

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“…When an infinitesimal deformation of the deformed AdS 2 geometry is considered, one would encounter a deformed Schwarzian derivative, though it seems difficult to determine what it is because there is no SL(2) invariance on the boundary in comparison to the standard setup studied in [12,29,30]. It is also interesting to study Yang-Baxter deformations of the Callan-Giddings-Harvey-Strominger (CGHS) model [79] by following [72,80,81].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Deformations of the Almheiri-Polchinski model

Kyono

Okumura

Yoshida

2017

J. High Energ. Phys.

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We study deformations of the Almheiri-Polchinski (AP) model by employing the Yang-Baxter deformation technique. The general deformed AdS 2 metric becomes a solution of a deformed AP model. In particular, the dilaton potential is deformed from a simple quadratic form to a hyperbolic function-type potential similarly to integrable deformations. A specific solution is a deformed black hole solution. Because the deformation makes the spacetime structure around the boundary change drastically and a new naked singularity appears, the holographic interpretation is far from trivial. The Hawking temperature is the same as the undeformed case but the Bekenstein-Hawking entropy is modified due to the deformation. This entropy can also be reproduced by evaluating the renormalized stress tensor with an appropriate counter-term on the regularized screen close to the singularity.

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“…13 Indeed, the first two parts of (5.1) can be determined on the analogy of abelian twists. For the detail of the derivation, see [64].…”

Section: Lax Pair For the General κ-Poincaré Deformationmentioning

confidence: 99%

“…The expression (5.8) always holds, but the classical r-matrix (4.1) was assumed for (5.9) . However, as shown in[64], the expression (5.9) is eventually valid for arbitrary classical r-matrices of Poicaré ⊗ Poincaré.…”

mentioning

confidence: 94%

Yang-Baxter sigma models and Lax pairs arising from κ-Poincaré r-matrices

Borowiec¹,

Kyono²,

Lukierski³

et al. 2016

J. High Energ. Phys.

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We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes arising from classical r-matrices associated with κ-deformations of the Poincaré algebra. These classical κ-Poincaré r-matrices describe three kinds of deformations: 1) the standard deformation, 2) the tachyonic deformation, and 3) the light-cone deformation. For each deformation, the metric and two-form B-field are computed from the associated r-matrix. The first two deformations, related to the modified classical Yang-Baxter equation, lead to T-duals of dS 4 and AdS 4 , respectively. The third deformation, associated with the homogeneous classical Yang-Baxter equation, leads to a time-dependent pp-wave background. Finally, we construct a Lax pair for the generalized κ-Poincaré r-matrix that unifies the three kinds of deformations mentioned above as special cases.

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Lax pairs for deformed Minkowski spacetimes

Cited by 10 publications

References 84 publications

Supercoset construction of Yang–Baxter-deformed AdS5×S5 backgrounds

Supercoset construction of Yang–Baxter-deformed AdS5×S5 backgrounds

Deformations of the Almheiri-Polchinski model

Yang-Baxter sigma models and Lax pairs arising from κ-Poincaré r-matrices

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