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SIGMA, 2016, Volume 12, 068, 36 pages (Mi sigma1150)  

This article is cited in 9 scientific papers (total in 9 papers)

Exact Renormalisation Group Equations and Loop Equations for Tensor Models

Thomas Krajewskia, Reiko Toriumib

a Aix Marseille Université, Université de Toulon, CNRS, CPT, UMR 7332, 13288 Marseille, France
b Department of Physics, University of California Berkeley, USA

Abstract: In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading order expectation values of observables in tensor models. Furthermore, we use the exact renormalisation group equations to establish a suitable scaling dimension for interactions in Abelian tensorial group field theories with a closure constraint. We also present analogues of the loop equations for tensor models.

Keywords: tensor models; group field theory; large $N$ limit; exact renormalisation equation.

Funding Agency Grant Number
Agence Nationale de la Recherche JCJC CombPhysMat2Tens
T.K. is partially supported by the grant “ANR JCJC CombPhysMat2Tens”.


DOI: https://doi.org/10.3842/SIGMA.2016.068

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Full text: http://www.emis.de/journals/SIGMA/2016/068/
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Bibliographic databases:

ArXiv: 1603.00172
MSC: 81T17; 81T18
Received: February 29, 2016; in final form July 5, 2016; Published online July 14, 2016
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Citation: Thomas Krajewski, Reiko Toriumi, “Exact Renormalisation Group Equations and Loop Equations for Tensor Models”, SIGMA, 12 (2016), 068, 36 pp.

Citation in format AMSBIB
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\by Thomas~Krajewski, Reiko~Toriumi
\paper Exact Renormalisation Group Equations and Loop Equations for~Tensor Models
\jour SIGMA
\yr 2016
\vol 12
\papernumber 068
\totalpages 36
\mathnet{http://mi.mathnet.ru/sigma1150}
\crossref{https://doi.org/10.3842/SIGMA.2016.068}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84984799735}


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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. Sylvain Carrozza, “Flowing in Group Field Theory Space: a Review”, SIGMA, 12 (2016), 070, 30 pp.  mathnet  crossref
    2. S. Carrozza, V. Lahoche, D. Oriti, “Renormalizable group field theory beyond melonic diagrams: an example in rank four”, Phys. Rev. D, 96:6 (2017), 066007  crossref  mathscinet  isi
    3. S. Carrozza, V. Lahoche, “Asymptotic safety in three-dimensional $\mathrm{SU}(2)$ group field theory: evidence in the local potential approximation”, Class. Quantum Gravity, 34:11 (2017), 115004  crossref  mathscinet  zmath  isi
    4. C. I. Perez-Sanchez, “Surgery in colored tensor models”, J. Geom. Phys., 120 (2017), 262–289  crossref  mathscinet  zmath  isi
    5. 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
    6. J. Ben Geloun, R. Toriumi, “Renormalizable enhanced tensor field theory: the quartic melonic case”, J. Math. Phys., 59:11 (2018), 112303  crossref  mathscinet  zmath  isi  scopus
    7. 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
    8. 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
    9. Krajewski T., Laudonio M., Pascalie R., Tanasa A., “Non-Gaussian Disorder Average in the Sachdev-Ye-Kitaev Model”, Phys. Rev. D, 99:12 (2019), 126014  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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