2D fuzzy anti-de Sitter space from matrix models

Jurman, Danijel; Steinacker, Harold

doi:10.1007/jhep01(2014)100

Cited by 51 publications

(74 citation statements)

References 44 publications

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“…[12][13][14][15][16][17]. Even compact solutions were found in [18,19], where it was pointed out that the induced metric on the brane can change from Euclidean to Minkowski signature.…”

Section: Jhep02(2018)033mentioning

confidence: 98%

“…It is natural to wonder about de Sitter branes. There are indeed candidates for fuzzy de Sitter space based on the principal series representations of SO(4, 1) [12,32,[39][40][41][42], some of which should be solutions of the matrix model for m 2 0 = m 2 ; see also [43] for related work. However then the effective metric would coincide with the induced one, without BB.…”

Section: Discussionmentioning

confidence: 99%

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Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Steinacker

2018

J. High Energ. Phys.

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We present simple solutions of IKKT-type matrix models that can be viewed as quantized homogeneous and isotropic cosmological space-times, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble parameter is singular at the BB, and becomes small at late times. There is no singularity from the target space point of view, and the brane is Euclidean "before" the BB. Both recollapsing and expanding universe solutions are obtained, depending on the mass parameters.

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“…[12][13][14][15][16][17]. Even compact solutions were found in [18,19], where it was pointed out that the induced metric on the brane can change from Euclidean to Minkowski signature.…”

Section: Jhep02(2018)033mentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Steinacker

2018

J. High Energ. Phys.

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“…Finally, we recall that other different quantum (A)dS deformations have been obtained by working in a conformal basis instead of a pure kinematical one, for instance, (3, 2) [100, 101] and (4, 2) [47,[102][103][104], and the Drinfel' d-Jimbo quantum AdS space at roots of unity has been worked out in [105]. Also, other fuzzy [106,107] and covariant [44] noncommutative (A)dS spacetimes have also been constructed.…”

Section: Discussionmentioning

confidence: 99%

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

Ballesteros

Bruno

Herranz

2017

Advances in High Energy Physics

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The -deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel' d-double and the Poisson-Lie structure underlying the -deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson-Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize the -Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of "duality" between the cosmological constant and the Planck scale is also envisaged.

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“…This space is a similar construction to the R 3 λ , i.e. a foliation of the three-dimensional Minkowski spacetime by fuzzy hyperboloids 1 [51]. Since the coordinates are matrices in reducible representations of SU(1,1), they are written in block diagonal form of irreducible representations, with each block being a fuzzy hyperboloid, which means that the space we end up with is a foliation of the three-dimensional Minkowski spacetime by fuzzy hyperboloids.…”

Section: Introductionmentioning

confidence: 99%

Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

Jurman¹,

Manolakos²,

Manousselis³

et al. 2018

Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017)

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We plan to translate the successful description of three-dimensional gravity as a gauge theory in the noncommutative framework, making use of the covariant coordinates. We consider two specific three-dimensional fuzzy spaces based on SU(2) and SU(1,1), which carry appropriate symmetry groups. These are the groups we are going to gauge in order to result with the transformations of the gauge fields (dreibein, spin connection and two extra Maxwell fields due to noncommutativity), their corresponding curvatures and eventually determine the action and the equations of motion. Finally, we verify their connection to three-dimensional gravity.

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2D fuzzy anti-de Sitter space from matrix models

Cited by 51 publications

References 44 publications

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

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