Emergent geometry and gravity from matrix models: an introduction

Steinacker, Harold

doi:10.1088/0264-9381/27/13/133001

Cited by 211 publications

(418 citation statements)

References 114 publications

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“…The BB arises from a signature change in the effective metric, taking into account the quantized 4-volume form which arises from the non-commutative structure of the brane. The point is that the effective metric on the brane M is not the induced metric, but involves the Poisson structure on the brane in an essential way 2 [9][10][11]. The Poisson structure gives rise to the frame bundle, and its flux provides the measure for the integration on M. This determines the conformal factor of the metric which is singular at the location of signature change, leading to a singular initial expansion.…”

Section: Jhep02(2018)033mentioning

confidence: 99%

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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Section: Jhep02(2018)033mentioning

confidence: 99%

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

Steinacker

2018

J. High Energ. Phys.

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“…This new aspect of symmetry should be explored further in the context of the general idea that spacetime and gravity are emergent phenomena [57][58][59][60][61][62][63][64][65][66][67][68] .…”

Section: Summary Discussion and Future Prospectsmentioning

confidence: 99%

Tensor models and 3-ary algebras

Sasakura¹

2011

Journal of Mathematical Physics

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Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a tensor with three indices as its only dynamical variable. The algebraic structure is studied mainly from the perspective of 3-ary algebras. It is shown that the tensor models have algebraic expressions, and that their symmetries are represented by 3-ary algebras. It is also shown that the 3-ary algebras of coordinates, which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with Gaussian functions in the tensor models, form Lie triple systems, and the associated Lie algebras are shown to agree with those of the Snyder's noncommutative spacetimes. The Poincare transformations of the coordinates on the fuzzy flat spacetimes are shown to be generated by 3-ary algebras.

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“…A series of interesting works along this line has recently been conducted by Steinacker and his collaborators [25][26][27]. See his recent review [28] and references therein. Also, there are many closely related works [29][30][31][32][33][34][35][36][37].…”

Section: Outline Of the Papermentioning

confidence: 99%

“…Now, consider a flow φ t : U × [0, 1] → M generated by the vector field X t satisfying Eq. (28). Under the action of φ ǫ with an infinitesimal ǫ, one finds that the point p ∈ U whose coordinates are y µ is mapped…”

Section: A the Equivalence Principle From Symplectic Geometrymentioning

confidence: 99%

Quantum gravity from noncommutative spacetime

Lee

Yang

2014

Journal of the Korean Physical Society

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We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U (1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U (1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative ⋆-algebra) of quantum gravity.

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Emergent geometry and gravity from matrix models: an introduction

Cited by 211 publications

References 114 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

Tensor models and 3-ary algebras

Quantum gravity from noncommutative spacetime

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