Abstract
This note fills a gap in the article (Ben Geloun and Rivasseau, Commun Math Phys 318:69–109, 2013). We provide the proof of Eq. (82) of Lemma 5 in Ben Geloun and Rivasseau (Commun Math Phys 318:69–109, 2013) and thereby complete its power-counting analysis with a more precise next-to-leading-order estimate.
Similar content being viewed by others
References
Ben Geloun J., Rivasseau V.: A Renormalizable 4-Dimensional Tensor Field Theory. Commun. Math. Phys. 318, 69–109 (2013)
Rivasseau V.: Quantum Gravity and Renormalization: The Tensor Track. AIP Conf. Proc. 1444, 18 (2011)
Ben Geloun, J.: Two- and four-loop β-functions of rank-4 renormalizable tensor field theories. Class. Quantum Grav. 29, 235011 (2012)
Ben Geloun, J., Samary, D.O.: 3D Tensor Field Theory: Renormalization and One-loop β-functions. http://arxiv.org/abs/1201.0176v2 [hep-th], 2012
Bonzom V., Gurau R., Rivasseau V.: Random tensor models in the large N limit: Uncoloring the colored tensor models. Phys. Rev. D 85, 084037 (2012)
Gurau R., Ryan J.P.: Colored Tensor Models - a review. SIGMA 8, 020 (2012)
Ben Geloun, J., Livine, E.R.: Some classes of renormalizable tensor models. http://arxiv.org/abs/1207.0416v1 [hep-th], 2012
Carrozza, S., Oriti, D., Rivasseau, V.: Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions. http://arxiv.org/abs/1207.6734v2 [hep-th], 2012
Gurau R.: The Double Scaling Limit in Arbitrary Dimensions: A Toy Model. Phys. Rev. D 84, 124051 (2011)
Gurau R., Universality for Random Tensors. http://arxiv.org/abs/1111.0519v3 [math.PR], 2012
Bonzom V., Gurau R., Riello A., Rivasseau V.: Critical behavior of colored tensor models in the large N limit. Nucl. Phys. B 853, 174 (2011)
Gurau R.: The complete 1/N expansion of colored tensor models in arbitrary dimension. Ann. H. Poincare 13, 399 (2012)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by A. Connes
Commun. Math. Phys. 318, no 1, 69–109 (2013)
The online version of the original article can be found under doi:10.1007/s00220-012-1549-1.
Rights and permissions
About this article
Cite this article
Ben Geloun, J., Rivasseau, V. Addendum to: A Renormalizable 4-Dimensional Tensor Field Theory. Commun. Math. Phys. 322, 957–965 (2013). https://doi.org/10.1007/s00220-013-1703-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-013-1703-4