Hidden Yangian symmetry in sigma model on squashed sphere

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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.

Section: Jhep03(2017)173mentioning

confidence: 93%

Deformations of the Almheiri-Polchinski model

Kyono

Okumura

Yoshida

2017

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“…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%

“…The first example is 17) and the resulting metric and B-field are given by This r-matrix is non-Abelian. The Ricci scalar and Riemann square vanish.…”

Section: One-parameter Deformationsmentioning

confidence: 99%

Yang-Baxter deformations of Minkowski spacetime

Matsumoto

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.

“…These are Yang's r-matrix of rational type, 24) and satisfy the classical Yang-Baxter equation (3.36). Note that it is independent of C.…”

Section: Jhep08(2014)110mentioning

confidence: 99%

“…Deformed target spaces are not represented by symmetric cosets, but typically by non-symmetric cosets (For arguments on some examples, see [23]). A particularly simple and tractable example is squashed S 3 and its integrable structure has been studied intensively [24][25][26][27][28][29][30][31][32][33][34][35][36]. In the recent, a generalization to higher dimensions has succeeded for arbitrary compact Lie groups and symmetric cosets [37], by following the Yang-Baxter sigma model description [38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

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

Kameyama

Yoshida

2014

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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.