Abstract
In this paper we analyze the multi-matrix model arising from the intermediate field representation of the tensor model with all quartic melonic interactions. We derive the saddle point equation and the Schwinger-Dyson constraints. We then use them to describe the leading and next-to-leading eigenvalues distribution of the matrices.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Ambjørn, B. Durhuus and T. Jonsson, Three-dimensional simplicial quantum gravity and generalized matrix models, Mod. Phys. Lett. A 6 (1991) 1133 [INSPIRE].
N. Sasakura, Tensor model for gravity and orientability of manifold, Mod. Phys. Lett. A 6 (1991) 2613 [INSPIRE].
P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 2-D Gravity and random matrices, Phys. Rept. 254 (1995) 1 [hep-th/9306153] [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
C. Itzykson and J.B. Zuber, The Planar Approximation. 2., J. Math. Phys. 21 (1980) 411 [INSPIRE].
B. Eynard, Topological expansion for the 1-Hermitian matrix model correlation functions, JHEP 11 (2004) 031 [hep-th/0407261] [INSPIRE].
B. Eynard and N. Orantin, Algebraic methods in random matrices and enumerative geometry, arXiv:0811.3531 [INSPIRE].
R. Gurau, Colored Group Field Theory, Commun. Math. Phys. 304 (2011) 69 [arXiv:0907.2582] [INSPIRE].
R. Gurau, The complete 1/N expansion of colored tensor models in arbitrary dimension, Annales Henri Poincaré 13 (2012) 399 [arXiv:1102.5759] [INSPIRE].
V. Bonzom, R. Gurau and V. Rivasseau, Random tensor models in the large-N limit: Uncoloring the colored tensor models, Phys. Rev. D 85 (2012) 084037 [arXiv:1202.3637] [INSPIRE].
V. Bonzom, R. Gurau, A. Riello and V. Rivasseau, Critical behavior of colored tensor models in the large-N limit, Nucl. Phys. B 853 (2011) 174 [arXiv:1105.3122] [INSPIRE].
W. Kaminski, D. Oriti and J.P. Ryan, Towards a double-scaling limit for tensor models: probing sub-dominant orders, New J. Phys. 16 (2014) 063048 [arXiv:1304.6934] [INSPIRE].
S. Dartois, R. Gurau and V. Rivasseau, Double Scaling in Tensor Models with a Quartic Interaction, JHEP 09 (2013) 088 [arXiv:1307.5281] [INSPIRE].
R. Gurau and G. Schaeffer, Regular colored graphs of positive degree, arXiv:1307.5279.
V. Bonzom, R. Gurau, J.P. Ryan and A. Tanasa, The double scaling limit of random tensor models, JHEP 09 (2014) 051 [arXiv:1404.7517] [INSPIRE].
V. Bonzom, R. Gurau and V. Rivasseau, The Ising Model on Random Lattices in Arbitrary Dimensions, Phys. Lett. B 711 (2012) 88 [arXiv:1108.6269] [INSPIRE].
V. Bonzom, R. Gurau and M. Smerlak, Universality in p-spin glasses with correlated disorder, J. Stat. Mech. Theor. Exp. 2013 (2013) L02003 [arXiv:1206.5539].
R. Gurau, The 1/N Expansion of Tensor Models Beyond Perturbation Theory, Commun. Math. Phys. 330 (2014) 973 [arXiv:1304.2666] [INSPIRE].
S. Dartois, A Givental-like Formula and Bilinear Identities for Tensor Models, arXiv:1409.5621 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1409.5751
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Nguyen, V.A., Dartois, S. & Eynard, B. An analysis of the intermediate field theory of T4 tensor model. J. High Energ. Phys. 2015, 13 (2015). https://doi.org/10.1007/JHEP01(2015)013
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2015)013