Quantum gravity and renormalization: The tensor track

Rivasseau, Vincent

doi:10.1063/1.4715396

Cited by 93 publications

(140 citation statements)

References 77 publications

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“…If we take this analogy seriously for the case of quantum gravity and quantum cosmology, it would mean that a high-curvature (presumably Planckian) regime cannot be described by a state consisting of near-flat, weakly interacting building blocks of geometry. Instead, one might expect a quantum phase transition, presumably a transition from a pre-geometric phase to a phase of an approximately smooth metric geometry -a scenario that often goes under the name of geometrogenesis [77,79]. Understanding this deep quantum-gravity regime will require methods that go beyond the ones used in this JHEP06(2014)013 paper, and that will be explored in future work.…”

Section: Jhep06(2014)013mentioning

confidence: 99%

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

132

256

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We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the 'condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

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Section: Jhep06(2014)013mentioning

confidence: 99%

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

132

256

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“…There are several approaches to this challenging issue. Tensor models belong to the promising candidates to understand quantum gravity (QG) in dimension D ≥ 3 [1]- [4]. Tensor models come from group field theory, which is a secondquantization of the loop quantum gravity, spin foam and certainly from matrix models [5].…”

Section: Introductionmentioning

confidence: 99%

Correlation functions of a just renormalizable tensorial group field theory: the melonic approximation

Samary¹,

Perez-Sanchez²,

Vignes-Tourneret³

et al. 2015

Class. Quantum Grav.

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The D-colored version of tensor models has been shown to admit a large N -limit expansion. The leading contributions result from so-called melonic graphs which are dual to the D-sphere. This is a note about the Schwinger-Dyson equations of the tensorial ϕ 4 5 -model (with propagator 1/p 2 ) and their melonic approximation. We derive the master equations for two-and four-point correlation functions and discuss their solution.Pacs numbers: 11.10. Gh,

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“…Recalling that ∆ = 1/q, the anomalous dimension for G c (τ) ∝ τ −2/q at small ω corresponds to the theory being just renormalizable in the tensor field theory sense [1].…”

Section: Two Point Functionmentioning

confidence: 99%

“…The tensor track [1] is an ongoing program which proposes to use random tensors [2] to progress on quantizing gravity. In this new issue of the franchise we focus on a brief and necessarily incomplete review of the most remarkable development of the last two years, namely the discovery and burgeoning study of holographic tensor models.…”

Section: Introductionmentioning

confidence: 99%

The Tensor Track V: Holographic Tensors

Delporte¹,

Rivasseau²

2018

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

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We review the fast developing subject of tensor models for the NAdS 2 /NCFT 1 holographic correspondence. We include a brief review of the Sachdev-Ye-Kitaev (SYK) model and then focus on the associated quantum mechanical tensor models (GW and CTKT). We examine their main features and how they compare with SYK. To end, we discuss different extensions: the large D limit of matrix-tensor models, the large N expansion of symmetric/antisymmetric tensors, the use of probes, the construction of a bilocal action for tensors, some attempts to extend the above models to higher dimensions and a proposal to break the tensor symmetry.

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Quantum gravity and renormalization: The tensor track

Cited by 93 publications

References 77 publications

Homogeneous cosmologies as group field theory condensates

Homogeneous cosmologies as group field theory condensates

Correlation functions of a just renormalizable tensorial group field theory: the melonic approximation

The Tensor Track V: Holographic Tensors

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