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

This article is cited in 18 scientific papers (total in 18 papers)

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.


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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

Citation: Vincent Rivasseau, “Random Tensors and Quantum Gravity”, SIGMA, 12 (2016), 069, 17 pp.

Citation in format AMSBIB
\by Vincent~Rivasseau
\paper Random Tensors and Quantum Gravity
\jour SIGMA
\yr 2016
\vol 12
\papernumber 069
\totalpages 17

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    This publication is cited in the following articles:
    1. Vincent Rivasseau, “Constructive Tensor Field Theory”, SIGMA, 12 (2016), 085, 31 pp.  mathnet  crossref
    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  crossref  mathscinet  isi
    3. J. Ben Geloun, S. Ramgoolam, “Tensor models, Kronecker coefficients and permutation centralizer algebras”, J. High Energy Phys., 2017, no. 11, 092  crossref  mathscinet  isi
    4. C. I. Perez-Sanchez, “Surgery in colored tensor models”, J. Geom. Phys., 120 (2017), 262–289  crossref  mathscinet  zmath  isi
    5. D. Oriti, “The universe as a quantum gravity condensate”, C. R. Phys., 18:3-4 (2017), 235–245  crossref  isi
    6. V. Rivasseau, “Loop vertex expansion for higher-order interactions”, Lett. Math. Phys., 108:5 (2018), 1147–1162  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  isi
    8. G. Chirco, D. Oriti, M. Zhang, “Ryu–Takayanagi formula for symmetric random tensor networks”, Phys. Rev. D, 97:12 (2018), 126002  crossref  mathscinet  isi
    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  crossref  mathscinet  zmath  isi
    10. V. Lahoche, D. O. Samary, “Unitary symmetry constraints on tensorial group field theory renormalization group flow”, Class. Quantum Gravity, 35:19 (2018), 195006  crossref  isi  scopus
    11. J. Ben Geloun, V. Rivasseau, “A renormalizable SYK-type tensor field theory”, Ann. Henri Poincare, 19:11 (2018), 3357–3395  crossref  mathscinet  zmath  isi  scopus
    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  crossref  isi  scopus
    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  crossref
    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  crossref  mathscinet  isi  scopus
    15. Glaser L. Steinhaus S., “Quantum Gravity on the Computer: Impressions of a Workshop”, Universe, 5:1 (2019), 35  crossref  mathscinet  isi  scopus
    16. Lahoche V. Samary D.O., “Progress in Solving the Nonperturbative Renormalization Group For Tensorial Group Field Theory”, Universe, 5:3 (2019), 86  crossref  isi  scopus
    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  crossref  isi
    18. Pithis A.G.A. Sakellariadou M., “Group Field Theory Condensate Cosmology: An Appetizer”, Universe, 5:6 (2019), 147  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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