Schwarzschild geometry emerging from matrix models

Blaschke, Daniel N.; Steinacker, Harold

doi:10.1088/0264-9381/27/18/185020

Cited by 20 publications

(36 citation statements)

References 36 publications

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“…This should eliminate any lingering doubts whether the geometries in the matrix model are sufficiently general for gravity. This construction is illustrated in [24] for the example of the Schwarzschild geometry.…”

Section: Realization Of Generic 4d Geometries In Matrix Modelsmentioning

confidence: 99%

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Non-commutative geometry and matrix models

Steinacker¹

2013

Proceedings of 3rd Quantum Gravity and Quantum Geometry School — PoS(QGQGS 2011)

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These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces (branes) is formulated, and their effective Riemannian geometry is elaborated. This class of configurations is preserved under small deformations, and is therefore appropriate for matrix models. A realization of generic 4-dimensional geometries is sketched, and the relation with spectral geometry and with noncommutative gauge theory is explained. In a second part, dynamical aspects of these matrix geometries are considered. The one-loop effective action for the maximally supersymmetric IKKT or IIB matrix model is discussed, which is well-behaved on 4-dimensional branes.

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Section: Realization Of Generic 4d Geometries In Matrix Modelsmentioning

confidence: 99%

“…9 It may happen that ω vanishes at certain locations, cf. [24]. This might be cured through compact extra dimensions.…”

Section: Deformations Of Embedded Nc Spacesmentioning

confidence: 99%

Non-commutative geometry and matrix models

Steinacker¹

2013

Proceedings of 3rd Quantum Gravity and Quantum Geometry School — PoS(QGQGS 2011)

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“…Multi-matrix models further arise in lower dimensional variants of the IKKT model [13], in the low energy dynamics of D-branes [14] and simple models of emergent geometry [15,16] and emergent gravity [17,18] and dimensionally reduced Yang-Mills models [19][20][21][22][23][24]. Many of these models will have regimes where commuting matrices play a rôle.…”

Section: Jhep08(2014)003mentioning

confidence: 99%

“…Next we focus on the reduction of the logarithmic kernel in (2.9). Using the rotational invariance of the distribution ρ p (x), we can write: 18) where the kernel K p (x, x ) is given by:…”

Section: Jhep08(2014)003mentioning

confidence: 99%

On the phase structure of commuting matrix models

Filev

O’Connor

2014

J. High Energ. Phys.

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We perform a systematic study of commutative SO(p) invariant matrix models with quadratic and quartic potentials in the large N limit. We find that the physics of these systems depends crucially on the number of matrices with a critical rôle played by p = 4. For p ≤ 4 the system undergoes a phase transition accompanied by a topology change transition. For p > 4 the system is always in the topologically trivial phase and the eigenvalue distribution is a Dirac delta function spherical shell. We verify our analytic work with Monte Carlo simulations.

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“…[1], [2], [3], [4], [5], [6], [7] Moreover, black hole and cosmological space-times were recovered in certain limits of matrix model solutions. [8], [9], [10], [11], [12], [13], [14] Matrix models were introduced by Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT) [15] and Banks, Fischler, Shenker, and Susskind (BFSS) [16] in order to represent nonperturbative aspects of string theory. Their application to black holes and cosmology holds the promise of including such nonperturbative effects.…”

Section: Introductionmentioning

confidence: 99%

Matrix model approach to cosmology

Chaney

Stern

2016

Phys. Rev. D

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We perform a systematic search for rotationally invariant cosmological solutions to matrix models, or more specifically the bosonic sector of Lorentzian IKKT-type matrix models, in dimensions d less than ten, specifically d = 3 and d = 5. After taking a continuum (or commutative) limit they yield d − 1 dimensional space-time surfaces, with an attached Poisson structure, which can be associated with closed, open or static cosmologies. For d = 3, we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit. Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit. The solutions provide for a matrix resolution of cosmological singularities. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the d = 3 solutions have analogues in higher dimensions. The case of d = 5, in particular, has the potential for yielding realistic four-dimensional cosmologies in the continuum limit. We find four-dimensional de Sitter dS 4 or anti-de Sitter AdS 4 solutions when a totally antisymmetric term is included in the matrix action. A nontrivial Poisson structure is attached to these manifolds which represents the lowest order effect of noncommutativity. For the case of AdS 4 , we find one particlular limit where the lowest order noncommutativity vanishes at the boundary, but not in the interior.

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Schwarzschild geometry emerging from matrix models

Cited by 20 publications

References 36 publications

Non-commutative geometry and matrix models

Non-commutative geometry and matrix models

On the phase structure of commuting matrix models

Matrix model approach to cosmology

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