The Tensor Track V: Holographic Tensors

Delporte, Nicolas; Rivasseau, Vincent

doi:10.22323/1.318.0218

Cited by 17 publications

(7 citation statements)

References 64 publications

(103 reference statements)

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“…Despite these many developments, which confirm that the field is growing and progressing fast, it remains clear that much more needs to be done, especially in the context of the physically more interesting GFT models and for what concerns the continuum limit of the same. In particular, the study of divergences of the new 4d GFT models for gravity, with similar techniques, and of their critical behaviour has recently started [101], but it remains in its infancy.…”

Section: A Selection Of Research Directions and Recent Resultsmentioning

confidence: 99%

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The microscopic dynamics of quantum space as a group field theory

Oriti

2012

Foundations of Space and Time

161

244

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We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status of the 4-dimensional extensions of this construction. We also briefly report on some recent results obtained in this approach, concerning both the mathematical definition of GFT models as bona fide field theories, and possible avenues towards extracting interesting physics from them.

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Section: A Selection Of Research Directions and Recent Resultsmentioning

confidence: 99%

“…As a result, ideas and tools from one become relevant to another, and trigger further progress. The group field theory (GFT) formalism [2][3][4]101] nicely captures this convergence of approaches and ideas. It is a generalization of the much studied matrix models for 2d quantum gravity and string theory [28].…”

mentioning

confidence: 90%

The microscopic dynamics of quantum space as a group field theory

Oriti

2012

Foundations of Space and Time

161

244

View full text Add to dashboard Cite

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“…Tensor models [1][2][3][4][5][6][7][8] have been put forward as a generalization of matrix models [9][10][11][12][13][14][15] to higher dimensions and provide a setting to explore random geometries with a view towards developing a quantum theory of gravity [1,2,[16][17][18][19]. The connection between random geometries and matrix models is established through discretizations of two-dimensional (2D) surfaces: the dual to a triangulation of the surface corresponds to a Feynman diagram of a matrix model, see figure 1.…”

Section: Introductionmentioning

confidence: 99%

Towards background independent quantum gravity with tensor models

Eichhorn¹,

Lumma²,

Koslowski³

et al. 2019

Class. Quantum Grav.

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We explore whether the phase diagram of tensor models could feature a pregeometric, discrete and a geometric, continuum phase for the building blocks of space. The latter are associated to rank d tensors of size N . We search for a universal large N scaling limit in a rank-3 model with real tensors that could be linked to a transition between the two phases. We extend the conceptual development and practical implementation of the flow equation for the pregeometric setting. This provides a pregeometric "coarse-graining" by going from many microscopic to few effective degrees of freedom by lowering N . We discover several candidates for fixed points of this coarse graining procedure, and specifically explore the impact of a novel class of interactions allowed in the real rank-3 model. In particular, we explain how most universality classes feature dimensional reduction, while one candidate, involving a tetrahedral interaction, might potentially be of relevance for threedimensional quantum gravity.

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“…But one would assume that the zero-mode effect persists in such models as well. Only if the tensorial degrees of freedom are not dynamic as in actual SYK-type models [42] the zero-mode effect would be absent. It is therefore of interest to study the FRG of such models.…”

Section: Discussionmentioning

confidence: 99%

(No) phase transition in tensorial group field theory

Pithis,

Thürigen

2020

Preprint

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Continuum spacetime is expected to emerge via phase transition in discrete approaches to quantum gravity. A promising example are tensorial and group field theories but their phase diagram remains an open issue. The results of recent attempts in terms of the functional renormalization group method remain inconclusive since they are restricted to truncations of low order.We overcome this barrier with a local-potential approximation for U(1) tensor fields at arbitrary rank r focusing on a specific class of so-called cyclic-melonic interactions. Projecting on constant field configurations, we obtain the full set of renormalization-group flow equations. At large scales we find equivalence with r − 1 dimensional O(N ) scalar field theory in the large-N limit, modified by a tensor-specific, relatively large anomalous dimension. As a consequence, in the large-volume limit there is a non-Gaussian fixed point with special non-integer critical exponents for rank r = 4 but not else. However, on small scales we find equivalence with the corresponding scalar field theory with vanishing dimension, thus no phase transition. This is confirmed by numerical analysis of the full non-autonomous equations where we always find symmetry restoration.The essential reason for this effect are isolated zero modes. This result should therefore be true for tensor field theories on any compact domain and including any tensor-invariant interactions. As a consequence, we expect that group field theory on a non-compact group will be necessary to describe gravitational degrees of freedom in a quantum regime together with a phase transition to continuum spacetime.

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The Tensor Track V: Holographic Tensors

Cited by 17 publications

References 64 publications

The microscopic dynamics of quantum space as a group field theory

The microscopic dynamics of quantum space as a group field theory

Towards background independent quantum gravity with tensor models

(No) phase transition in tensorial group field theory

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