Geometrogenesis under quantum graphity: Problems with the ripening universe

Wilkinson, Samuel A.; Greentree, Andrew D.

doi:10.1103/physrevd.92.084007

Cited by 4 publications

(6 citation statements)

References 19 publications

(36 reference statements)

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“…where N is finite, V n stands for the interaction function of order n and m 2 and λ n are the mass and coupling constants. With this truncation and with an appropriate regulator it is possible to solve the Wetterich flow equation (45). In the case of quartic melonic interaction and by taking the standard modified Litim's regulator:…”

Section: Wetterich Flow Equationmentioning

confidence: 99%

“…The FRG equation allows to determine the fixed points and probably the phase transition. These phase transitions in the case of TGFT models may help to identify the emergence of general relativity and quantum mechanics through the pregeometrogenesis scenario [42]- [45]. Indeed, the way the quantum degrees of freedom are organized to shape a geometric structure which can be identified with a semi-classical space-time is one of the challenges for GFT approach.…”

Section: Introductionmentioning

confidence: 99%

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Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

Lahoche

Samary

2019

Universe

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This manuscript aims at giving new advances on the functional renormalization group applied to the tensorial group field theory. It is based on a series of our three papers [arXiv:1803.09902], [arXiv:1809.00247] and [arXiv:1809.06081]. We consider the polynomial Abelian U (1) d models without closure constraint. More specifically, we discuss the case of the quartic melonic interaction. We present a new approach, namely the effective vertex expansion method, to solve the exact Wetterich flow equation, and investigate the resulting flow equations, specially regarding the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward-Takahashi identities, and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a first order phase transition into the reduced phase space given by the Ward constraint.

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Section: Wetterich Flow Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

Lahoche

Samary

2019

Universe

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“…In particular, we strengthen the conclusions about the existence of a non-trivial fixed point in the phase-space, which behaves like a Wilson-Fisher fixed point. The occurrence of such a fixed point has been considered as an important feature because it advocate a phase transition, which plays an important role in the space-time emergence following the geometrogenesis scenario (see introduction or [57]- [59] for more details).…”

Section: Improved φ 4 Truncationmentioning

confidence: 99%

Unitary symmetry constraints on tensorial group field theory renormalization group flow

Lahoche

Samary

2018

Class. Quantum Grav.

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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 flow for quartic melonic tensorial group field theories. Using the unitary invariance of the interactions, we provide a set of Ward-Takahashi identities which leads to relations between correlation functions. There are numerous reasons to consider such Ward identities in the functional renormalization group. Their compatibility along the flow provides a non-trivial constraint on the reliability of the approximation schemes used in the non-perturbative regime, especially on the truncation and the choice of the regulator. We establish the so called structure equations in the melonic sector and in the symmetric phase. As an example we consider the T 4 5 TGFT model without gauge constraint. The Wetterich flow equation is given and the way to improve the truncation on the effective action is also scrutinized.

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“…It can also be viewed as a new proposal for quantum field theories based on a Feynman path integral, which generates random graphs describing simplicial pseudo manifolds. It aims at providing a content to a phase transition called geometrogenesis scenario by relating a discrete quantum pregeometric phase of our spacetime to the classical continuum limit consistent with Einstein GR [44]- [46]. In short, within this approach, our spacetime and its geometry has to be reconstructed or must emerge from more fundamental and discrete degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Nonperturbative renormalization group beyond the melonic sector: The effective vertex expansion method for group fields theories

2018

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Tensor models admit the large N limit dominated by the graphs called melons. The melons are caracterized by the Gurau number = 0 and the amplitude of the Feynman graphs are proportional to N − . Other leading order contributions i.e.> 0 called pseudomelons 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 [arXiv:1803.09902], in which only the melonic sector have 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, that 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 non-trivial constraints in the approximation shemes. In the symmetric phase the Wetterich flow equation is given and the numerical solution is studied. 1 vincent.lahoche@cea.fr 2 dine.ousmanesamary@cipma.uac.bj An important notion for tensorial Feynman diagrams is the notion of faces, whose we recall in the following definition:Definition 2 A face is defined as a maximal and bicolored connected subset of lines, necessarily including the color 0. We distinguish two cases:• The closed or internal faces, when the bicolored connected set correspond to a cycle.3 Strictly speaking the term "quantum" is abusive, we should talk about statistical model, or quantum field theory in the euclidean time.

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Geometrogenesis under quantum graphity: Problems with the ripening universe

Cited by 4 publications

References 19 publications

Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

Unitary symmetry constraints on tensorial group field theory renormalization group flow

Nonperturbative renormalization group beyond the melonic sector: The effective vertex expansion method for group fields theories

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