Functional renormalization group for the U(1)-T-5(6) tensorial group field theory with closure constraint

  title={Functional renormalization group for the U(1)-T-5(6) tensorial group field theory with closure constraint},
  author={Vincent Lahoche and Dine Ousmane Samary},
  journal={Physical Review D},
This paper is focused on the functional renormalization group applied to the $T_5^6$ tensor model on the Abelian group $U(1)$ with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV… 

Figures and Tables from this paper

Ward-constrained melonic renormalization group flow for the rank-four ϕ6 tensorial group field theory
The nontrivial fixed point discovered for $\phi^4$-marginal couplings in tensorial group field theories have been showed to be incompatible with Ward-Takahashi identities. In this previous analysis
Unitary symmetry constraints on tensorial group field theory renormalization group flow
Renormalization group methods are an essential ingredient in the study of nonperturbative problems of quantum field theory. This paper deal with the symmetry constraints on the renormalization group
No Ward-Takahashi identity violation for Abelian tensorial group field theories with a closure constraint
This paper aims at investigating the nonperturbative functional renormalization group for tensorial group field theories with nontrivial kinetic action and closure constraint. We consider the quartic
Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
We study the functional renormalization group of a three-dimensional tensorial Group Field Theory (GFT) with gauge group SU(2). This model generates (generalized) lattice gauge theory amplitudes, and
Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory
This manuscript aims at giving new advances on the functional renormalization group applied to the tensorial group field theory. It is based on the series of our three papers (Lahoche, et al., Class.
Functional renormalization group analysis of rank-3 tensorial group field theory: The full quartic invariant truncation
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
Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
We prove the renormalizability of a gauge-invariant, four-dimensional GFT model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N
Non-perturbative Renormalization Group of a U (1) Tensor Model
This paper aims at giving some comment on our new development on the functional renormalization group applied to the U(1) tensor model previously studied in [Phys. Rev. D 95, 045013 (2017)]. Using
Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
We introduce a new family of tensorial field theories by coupling different fields in a nontrivial way, with a view towards the investigation of the coupling between matter and gravity in the quantum


Functional renormalization group approach for tensorial group field theory: a rank-6 model with closure constraint
We develop the functional renormalization group formalism for a tensorial group field theory with closure constraint, in the case of an Abelian just renormalizable model with quartic interactions.
Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
We study the renormalization of a general field theory on the 2-sphere with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power counting for arbitrary
Discrete renormalization group for SU(2) tensorial group field theory
This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th] (Commun. Math. Phys. 330, 581-637). It is a
Functional renormalisation group approach for tensorial group field theory: a rank-3 model
A bstractWe set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1)3, endowed with a kinetic term
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for
Renormalization of an Abelian tensor group field theory: solution at leading order
A bstractWe study a just-renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which
Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions
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 interactions up to
Nontrivial UV behavior of rank-4 tensor field models for quantum gravity
We investigate the universality classes of rank-4 colored bipartite U(1) tensor field models near the Gaussian fixed point with the functional renormalization group. In a truncation that contains all
Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the
3D Tensor Field Theory: Renormalization and One-Loop β-Functions
We prove that the rank 3 analogue of the tensor model defined in Ben Geloun and Rivasseau (Commun Math Phys, arXiv:1111.4997 [hep-th], 2012) is renormalizable at all orders of perturbation. The proof