Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Mathematical Physics

Renormalizable Models in Rank $${d \geq 2}$$ d ≥ 2 Tensorial Group Field Theory

Joseph Ben Geloun

Published Aug 22, 2014• 83 citations
Publisher
DOI
10.1007/s00220-014-2142-6

Related papers

Renormalization in Tensorial Group Field Theories

Sylvain Carrozza

Frontiers of Fundamental Physics 14 (FFP14)•Jan 1, 2014•0 citations

Transition of Ground State of Boson-Fermion Model and Renormalizable Field Theory (Applications of Renormalization Group Methods in Mathematical Sciences)

Masao Hirokawa

数理解析研究所講究録•Jul 1, 2002•0 citations

A Renormalizable SYK-Type Tensor Field Theory

Joseph Ben Geloun, Vincent Rivasseau

arXiv:1711.05967•Annales Henri Poincaré•Aug 17, 2018•17 citations

Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions

Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau

We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.

•Mar 27, 2013•110 citations

Renormalization in tensor Group Field Theory

Fabien Vignes-Tourneret

•Mar 17, 2014•0 citations

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

Joseph Ben Geloun, Tim Andreas Koslowski, Daniele Oriti +1 more

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.

arXiv:1805.01619•Physical review. D/Physical review. D.•Jun 29, 2018•43 citations
Renormalizable Models in Rank d≥2{d \geq 2}d≥2 d ≥ 2 Tensorial Group Field Theory
We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.
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.