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This manuscript reports the first order β-functions of recently proved just renormalizable random tensor models endowed with a φ(1)d gauge invariance. The models that we consider are polynomial Abelian φ64 and φ56 models. We show in this work that both models are asymptotically free in the UV. [ABSTRACT FROM AUTHOR]

This paper aims at giving a novel approach to investigate the behavior of the renormalization group flow for tensorial group field theories to all order of the perturbation theory. From an appropriate choice of the kinetic kernel, we build an infinite family of just-renormalizable models, for tensor fields with arbitrary rank d. Investigating the large d-limit, we show that the self-energy melonic amplitude is decomposed as a product of loop-vertex functions depending only on dimensionless mass. The corresponding melonic amplitudes may be mapped as trees in the so-called Hubbard-Stratonivich representation, and we show that only trees with edges of different colors survive in the large d-limit. These two key features allow to resum the perturbative expansion for self energy, providing an explicit expression for arbitrary external momenta in terms of Lambert function. Finally, inserting this resummed solution into the Callan-Symanzik equations, and taking into account the strong relation between two and four point functions arising from melonic Ward-Takahashi identities, we then deduce an explicit expression for relevant and marginal β-functions, valid to all orders of the perturbative expansion. By investigating the solutions of the resulting flow, we conclude about the nonexistence of any fixed point in the investigated region of the full phase space. [ABSTRACT FROM AUTHOR]

The standard nonperturbative approaches of renormalization group for tensor models are generally focused on a purely local potential approximation (i.e., involving only generalized traces and products of them) and are showed to strongly violate the modified Ward identities. This paper is a continuation of our recent contribution [Phys. Rev. D 101, 106015 (2020), intended to investigate the approximation schemes compatible with Ward identities and constraints between 2n-points observables in the large N limit. We consider separately two different approximations: In the first one, we try to construct a local potential approximation from a slight modification of the Litim regulator, so that it remains optimal in the usual sense, and preserves the boundary conditions in deep UV and deep IR limits. In the second one, we introduce derivative couplings in the truncations and show that the compatibility with Ward identities implies strong relations between β functions, allowing one to close the infinite hierarchy of flow equations in the nonbranching sector, up to a given order in the derivative expansion. Finally, using an exact relation between correlations functions in large N limit, we show that strictly local truncations are insufficient to reach the exact value for the critical exponent, highlighting the role played by these strong relations between observables taking into account the behavior of the flow; and the role played by the multitrace operators, discussed in the two different approximation schemes. In both cases, we compare our conclusions to the results obtained in the literature and conclude that, at a given order, by taking into account the exact functional relations between observables like Ward identities in a systematic way, we can strongly improve the physical relevance of the approximation for an exact renormalization group equation. [ABSTRACT FROM AUTHOR]

The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this paper, we focus on matrix models and address the question of the compatibility between the approximations used to solve the exact renormalization group equation and the modified Ward identities coming from the regulator. We show in particular that standard local potential approximation strongly violates the Ward identities, especially in the vicinity of the interacting fixed point. Extending the theory space including derivative couplings, we recover an interacting fixed point with a critical exponent not so far from the exact result, but with a nonzero value for derivative couplings, evoking a strong dependence concerning the regulator. Finally, we consider a modified regulator, allowing to keep the flow not so far from the ultralocal region and recover the results of the literature up to a slight improvement. [ABSTRACT FROM AUTHOR]

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 regime. As a first step, we consider the simple case with two tensors of the same rank coupled together, with Dirac like a kinetic kernel. We focus especially on rank-3 tensors, which lead to a power counting just-renormalizable model, and interpret Feynman graphs as Ising configurations on random lattices. We investigate the renormalization group flow for this model, using two different and complementary tools for approximations, namely, the effective vertex expansion method and finite-dimensional vertex expansion for the flowing action. Due to the complicated structure of the resulting flow equations, we divided the work into two parts. In this first part, we only investigate the fundamental aspects on the construction of the model and the different ways to get tractable renormalization group equations, while their numerical analysis will be addressed in a companion paper. [ABSTRACT FROM AUTHOR]

This paper, in addition to our recent works, intends to improve and give in detail the behavior of the Wetterich flow equations in the physical theory space. We focus on the local potential approximation and present a new framework of investigation, namely the effective vertex expansion coupled with Ward's identities for quartic melonic interactions, allowing us to consider infinite sectors rather than finite dimensional subspaces of the full theory space. The flow behavior in the vicinity of the Gaussian fixed point and the correction given by the effective vertex expansion is also analyzed. The dynamical constrained flow allows us to identify the influence of the number of melonic interactions related to the existence of divergence at which the possible first order phase transition may be identified is studied. Comparing our results using the formalism of Callan Symanzik equation is also scrutinized. [ABSTRACT FROM AUTHOR]

Tensor models admit the large N limit dominated by the graphs called melons. The melons are characterized by the Gurau number ϖ=0 and the amplitude of the Feynman graphs are proportional to N-ϖ. Other leading order contributions, i.e., ϖ>0 called pseudo-melons, can be taken into account in the renormalization program. The following paper deals with the renormalization group for a U(1)-tensorial group field theory model taking into account these two sectors (melon and pseudo-melon). It generalizes a recent work [V. Lahoche and D. Ousmane Samary, Classical Quantum Gravity 35, 195006 (2018)], in which only the melonic sector has been studied. Using the power counting theorem the divergent graphs of the model are identified. Also, the effective vertex expansion is used to generate in detail the combinatorial analysis of these two leading order sectors. We obtained the structure equations, which help to improve the truncation in the Wetterich equation. The set of Ward-Takahashi identities is derived and their compactibility along the flow provides a nontrivial constraint in the approximation schemes. In the symmetric phase the Wetterich flow equation is given and the numerical solution is studied. [ABSTRACT FROM AUTHOR]

This paper is focused on the functional renormalization group applied to the T 56 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 completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory. [ABSTRACT FROM AUTHOR]

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 melonic just-renormalizable [U(1)]6 model and show that due to this closure constraint the first order Ward-Takahashi identity takes the trivial form as for the models with propagators proportional to identity. We then construct the new version of the effective vertex expansion applicable to this class of models, which in particular allows us to close the hierarchical structure of the flow equations in the melonic sector. As a consequence, there are no additional constraints on the flow equations, and then we can focus on the existence of the physical Wilson-Fisher fixed-points in the symmetric phase. [ABSTRACT FROM AUTHOR]