Functional renormalization group analysis of rank-3 tensorial group field theory: The full quartic invariant truncation

Geloun, Joseph Ben (Laboratoire d’Informatique de Paris Nord UMR CNRS 7030 Université Paris 13, 99 avenue J.-B. Clement, 93430 Villetaneuse, France) (International Chair in Mathematical Physics and Applications ICMPA—UNESCO Chair, 072 B.P. 50 Cotonou, Benin) ; Koslowski, Tim A. (Instituto de Ciencias Nucleaes, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, 04510 Ciudad de México, Distrito Federal, Mexico) ; Oriti, Daniele (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam-Golm, Germany) (II Institute for Theoretical Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany) ; Pereira, Antonio D. (Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany)

29 June 2018

Abstract: In this paper, we consider the complete momentum-independent quartic order truncation for the effective average action of a real Abelian rank-3 tensorial group field theory. This complete truncation includes nonmelonic as well as double-trace interactions. In the usual functional renormalization group perspective, the inclusion of more operators that belong to the underlying theory space corresponds to an improvement of the truncation of the effective average action. We show that the inclusion of nonmelonic and double-trace operators in the truncation brings subtleties. In particular, we discuss the assignment of scaling dimensions to the nonmelonic sector and how the inclusion of double-trace operators considerably changes the results for critical exponents with respect to those obtained when they are not included. We argue that this is not a particular problem of the present model by comparing the results with a pure tensor model. We discuss how these issues should be investigated in future work.

Published in: Physical Review D 97 (2018)
Published by: APS
DOI: 10.1103/PhysRevD.97.126018
arXiv: 1805.01619
License: CC-BY-4.0

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