Unified description for $$\kappa $$ κ -deformations of orthogonal groups

Borowiec, A.; Pachoł, Anna

doi:10.1140/epjc/s10052-014-2812-8

Cited by 28 publications

(46 citation statements)

References 69 publications

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“…It is rewarding that for the jordanian deformation a large subset of the deformed Poincaré generators are pseudo-hermitian for the same choice of an invertible hermitian η operator, see e.g. formula (19). Therefore, they are observable with respect to the η-modified inner product [38].…”

Section: Discussionmentioning

confidence: 99%

“…To be specific, in the large class of deformed Poincaré theories (which include, e.g., κ-Poincaré theories [1]- [3], Deformed Special Relativity theories [4,5], light-like noncommutativity in Very Special Relativity [6,7] and many other examples [8]- [10]) we focus on the Drinfel'd twist [11,12] deformations of a light-like direction. Due to this reason the deformations we consider here are based on the jordanian [13]- [15] and on the extended jordanian [16] twist (for physical applications of the Jordanian twist see [17,18] and, for the extended Jordanian twist, [19]- [24]).…”

Section: Introductionmentioning

confidence: 99%

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On light-like deformations of the Poincaré algebra

Kuznetsova

Toppan

2019

Eur. Phys. J. C

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We investigate the observational consequences of the light-like deformations of the Poincaré algebra induced by the jordanian and the extended jordanian classes of Drinfel'd twists. Twist-deformed generators belonging to a Universal Enveloping Algebra close nonlinear algebras. In some cases the nonlinear algebra is responsible for the existence of bounded domains of the deformed generators. The Hopf algebra coproduct implies associative nonlinear additivity of the multi-particle states. A subalgebra of twist-deformed observables is recovered whenever the twist-deformed generators are either hermitian or pseudo-hermitian with respect to a common invertible hermitian operator.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On light-like deformations of the Poincaré algebra

Kuznetsova

Toppan

2019

Eur. Phys. J. C

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“…Let us now return to the κ + branch. In this case the deformation parameter is 26) and once re-written in the new coordinates, the deformed NS sector takes the form:…”

Section: )mentioning

confidence: 99%

“…where a is a constant vector. When a is light-like (null), it is well documented, e. g. [26,27], that the r-matrix is a solution to the homogeneous CYBE, otherwise we get a solution to the modified CYBE. As we show in the appendix, starting from flat spacetime, the light-like κ-deformation leads to a "trivial" solution [28] of generalised supergravity 3 .…”

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confidence: 99%

Embedding the modified CYBE in supergravity

2018

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It has recently been demonstrated that given a generic solution, the Classical Yang-Baxter Equation (CYBE) emerges from supergravity via the open-closed string map, thus providing tangible evidence for the conjectured equivalence between supergravity equations of motion and the homogeneous CYBE. To date, study of this equivalence has largely been confined to the NS sector. In this work, we make two extensions. First, we revisit the transformation of the RR sector and clarify its precise role in the emergence of the CYBE. Secondly, we identify direct products of coset geometries as the only setting where the transformation permits embeddings of the modified CYBE. We illustrate our solution generating technique with deformations of AdS 3 ×S 3 ×M 4 , where M 4 = T 4 (K3) and S 3 ×S 1 , and explicitly construct one and two-parameter integrable q-deformations that are solutions to generalised supergravity.Over recent years, the Yang-Baxter σ-model [1-3] has emerged as a systematic way to construct integrable deformations of maximally symmetric AdS/CFT geometries. In principle this extends the scope of integrability techniques in holography to more realistic settings. Central to this approach is an r-matrix solution to the Classical Yang-Baxter Equation (CYBE). The Yang-Baxter σ-model was initially formulated in terms of r-matrix solutions to the modified CYBE, before it was later understood that there was a richer class of deformations based on r-matrix solutions to the homogeneous CYBE [4][5][6].Since there are fewer solutions to the modified CYBE, it is perfectly understandable that the corresponding supergravity solutions are rarer 1 . However, this appears to be a disproportionate rareness, since given an r-matrix solution to the modified CYBE, there is no guarantee a corresponding embedding in supergravity exists. This ultimately can be traced to the fact that such solutions are less natural from the supergravity perspective, as we will explain in due course.We recall from a series of recent papers [10-12] that Yang-Baxter deformations for rmatrices based on both the homogeneous and modified CYBE are described by an open-closed string map [14], where the deformation is specified by a bivector Θ that is an antisymmetric product of Killing vectors, or simply "bi-Killing". The joy of this map is it reduces the deformation to a single matrix inversion in the σ-model target space. Moreover, the map can be built into a powerful solution generating technique [13] for generalised supergravity [15,16]. This approach hinges on the assumption, explicitly checked case by case in [13,17], that the equations of generalised supergravity reduce to the CYBE, and once the homogeneous CYBE holds, so too do the equations of motion. In the process, Θ is identified with an r-matrix solution 2 .A step towards a proof of the equivalence between the equations of motion of generalised supergravity and the CYBE for deformations appeared in [17]. In particular, restricting to the NS sector, and geometries not supported by the NSNS two-form,...

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“…Let us start reviewing the construction of the lightlike deformed Poincaré algebra as a Hopf algebra following [24]. Then we will extend this procedure to the BMS algebra.…”

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confidence: 99%

κ-deformed BMS symmetry

et al. 2019

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We present the quantum κ-deformation of BMS symmetry, by generalizing the lightlike κ-Poincaré Hopf algebra. On the technical level our analysis relies on the fact that the lightlike κ-deformation of Poincaré algebra is given by a twist and the lightlike deformation of any algebra containing Poincaré as a subalgebra can be done with the help of the same twisting element. We briefly comment on the physical relevance of the obtained κ-BMS Hopf algebra as a possible asymptotic symmetry of quantum gravity.In the recent years there is a surge of interest in BMS symmetry at null infinity of asymptotically flat spacetimes [1], [2], [3]. This renewed interest in the seemingly exotic aspects of classical general relativity was fueled by the discovery of a surprising and close relationship between asymptotic symmetries and soft gravitons theorem [4] that, as it turned out, has its roots in Ward identities for supertranslations [5], [6]. Moreover, the gravitational memory effect [7] appears to be related to the two [8], so that there is a triangle of interrelationships, which vertices are BMS symmetry, Weinberg's soft graviton theorem, and the memory effect. The extensive discussion of these effects can be found in recent reviews [9] and [10].It has also been argued recently [11] that the similarity of null infinity and black hole horizon suggests that the charges associated with the BMS symmetry might be present at the black hole horizon, so that the black hole might have an infinite number of hairs, so-called soft hairs, in addition to the three classical one: mass, charge, and angular momentum. It was argued in [11] and [12] that the presence of these charges may help solving the black hole information paradox.In this letter we will investigate the properties of a κ-deformed generalization of the BMS symmetry. There are several reasons to be interested in such a generalization. The main one is that it is believed that investigations of κ-deformation might shed some light on the properties of elusive quantum gravity. The deformation parameter of κ-deformation of Poincaré algebra [13]-[17], see [18] for a recent review and more references, has dimension of mass, and therefore it is natural to identify it with Planck mass, or inverse Planck length, which in turn suggests a possible close relationship between this deformation and quantum gravity. In fact, it was shown in [19]

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Unified description for $$\kappa $$ κ -deformations of orthogonal groups

Cited by 28 publications

References 69 publications

On light-like deformations of the Poincaré algebra

On light-like deformations of the Poincaré algebra

Embedding the modified CYBE in supergravity

κ-deformed BMS symmetry

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