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 SIGMA, 2016, Volume 12, 069, 17 pages (Mi sigma1151)

Random Tensors and Quantum Gravity

Vincent Rivasseau

Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris XI, F-91405 Orsay Cedex, France

Abstract: We provide an informal introduction to tensor field theories and to their associated renormalization group. We focus more on the general motivations coming from quantum gravity than on the technical details. In particular we discuss how asymptotic freedom of such tensor field theories gives a concrete example of a natural “quantum relativity” postulate: physics in the deep ultraviolet regime becomes asymptotically more and more independent of any particular choice of Hilbert basis in the space of states of the universe.

Keywords: renormalization; tensor models; quantum gravity.

DOI: https://doi.org/10.3842/SIGMA.2016.069

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Full text: http://www.emis.de/journals/SIGMA/2016/069/
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ArXiv: 1603.07278
MSC: 60B20; 81T15; 81T16; 81T17; 82B28
Received: March 23, 2016; in final form July 6, 2016; Published online July 15, 2016
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Citation: Vincent Rivasseau, “Random Tensors and Quantum Gravity”, SIGMA, 12 (2016), 069, 17 pp.

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Vincent Rivasseau, “Constructive Tensor Field Theory”, SIGMA, 12 (2016), 085, 31 pp.
2. V. Lahoche, D. O. Samary, “Functional renormalization group for the $U(1)-T^6_5$ tensorial group field theory with closure constraint”, Phys. Rev. D, 95:4 (2017), 045013
3. J. Ben Geloun, S. Ramgoolam, “Tensor models, Kronecker coefficients and permutation centralizer algebras”, J. High Energy Phys., 2017, no. 11, 092
4. C. I. Perez-Sanchez, “Surgery in colored tensor models”, J. Geom. Phys., 120 (2017), 262–289
5. D. Oriti, “The universe as a quantum gravity condensate”, C. R. Phys., 18:3-4 (2017), 235–245
6. V. Rivasseau, “Loop vertex expansion for higher-order interactions”, Lett. Math. Phys., 108:5 (2018), 1147–1162
7. G. Chirco, D. Oriti, M. Zhang, “Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity”, Class. Quantum Gravity, 35:11 (2018), 115011
8. G. Chirco, D. Oriti, M. Zhang, “Ryu–Takayanagi formula for symmetric random tensor networks”, Phys. Rev. D, 97:12 (2018), 126002
9. A. Eichhorn, T. Koslowski, “Flowing to the continuum limit in tensor models for quantum gravity”, Ann. Inst. Henri Poincare D, 5:2 (2018), 173–210
10. V. Lahoche, D. O. Samary, “Unitary symmetry constraints on tensorial group field theory renormalization group flow”, Class. Quantum Gravity, 35:19 (2018), 195006
11. J. Ben Geloun, V. Rivasseau, “A renormalizable SYK-type tensor field theory”, Ann. Henri Poincare, 19:11 (2018), 3357–3395
12. V. Lahoche, D. O. Samary, “Nonperturbative renormalization group beyond the melonic sector: the effective vertex expansion method for group fields theories”, Phys. Rev. D, 98:12 (2018), 126010
13. Oriti D., “Spacetime as a quantum many-body system”, Many-body Approaches at Different Scales, A Tribute to Norman H. March on the Occasion of his 90th Birthday, 2018, 365–379
14. Eichhorn A. Koslowski T. Pereira A.D., “Status of Background-Independent Coarse Graining in Tensor Models For Quantum Gravity”, Universe, 5:2 (2019), 53
15. Glaser L. Steinhaus S., “Quantum Gravity on the Computer: Impressions of a Workshop”, Universe, 5:1 (2019), 35
16. Lahoche V. Samary D.O., “Progress in Solving the Nonperturbative Renormalization Group For Tensorial Group Field Theory”, Universe, 5:3 (2019), 86
17. Eichhorn A. Lumma J. Koslowski T. Pereira A.D., “Towards Background Independent Quantum Gravity With Tensor Models”, Class. Quantum Gravity, 36:15 (2019), 155007
18. Pithis A.G.A. Sakellariadou M., “Group Field Theory Condensate Cosmology: An Appetizer”, Universe, 5:6 (2019), 147
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