The Tensor Track: An Update

Rivasseau, Vincent

doi:10.1142/9789814518550_0011

Cited by 45 publications

(63 citation statements)

References 119 publications

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“…αβγ and X (2) αβγ in the following statement Proposition 5. Pertubatively, at second order in λ the symmetry solution of the equation (67) using the Cauchy principal value is given by…”

Section: λ 1−λmentioning

confidence: 96%

Closed equations of the two-point functions for tensorial group field theory

Samary

2014

Class. Quantum Grav.

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In this paper we provide the closed equations that satisfy two-point correlation functions of the rank 3 and 4 tensorial group field theory. The formulation of the present problem extends the method used by Grosse and Wulkenhaar in [arXiv 0909.1389] to the tensor case. Ward-Takahashi identities and Schwinger-Dyson equations are combined to establish a nonlinear integral equation for the two-point functions. In the 3D case the solution of this equation is given perturbatively at second order of the coupling constant.Pacs numbers: 11.10. Gh,

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Section: λ 1−λmentioning

confidence: 96%

Closed equations of the two-point functions for tensorial group field theory

Samary

2014

Class. Quantum Grav.

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“…This may not be the case. In fact, it is not expected to be the case in much GFT (and tensor models) literature, where instead the goal is to extract emergent continuum gravitational (thus geometric) physics from the collective behavior of the underlying microscopic degrees of freedom [46,49,50,59,60]. If the relation between the Renyi entropy of our states and the divergences of the underlying GFT is generic, as we expect, the former is probably not analytic in the coupling constant, and its value will be dictated by the most divergent contributions to the Feynman expansion of the GFT model, which are obviously growing with the number of interaction vertices involved, thus it will be ultimately dominated by higher powers of λ.…”

Section: Maximal Divergent Diagrams In the Linear Perturbation Ordermentioning

confidence: 99%

Group field theory and holographic tensor networks: dynamical corrections to the Ryu–Takayanagi formula

Chirco

Goeßmann

Oriti³

et al. 2020

Class. Quantum Grav.

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We introduce group field theory networks as a generalization of spin networks and of (symmetric) random tensor networks and provide a statistical computation of the Rényi entropy for a bipartite network state using the partition function of a simple interacting group field theory. The expectation value of the entanglement entropy is calculated by an expansion into stranded Feynman graphs and is shown to be captured by a Ryu-Takayanagi formula. For a simple interacting group field theory, we can prove the linear corrections, given by a polynomial perturbation of the Gaussian measure, to be negligible for a broad class of networks.

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“…s; p q cannot be diagonal for non vanishing means fields 4 . In the rest of this paper, we consider only the symmetric phase and the effective vertices then can be considered as the first terms correction in means field expansion like in (22).…”

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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The Tensor Track: An Update

Cited by 45 publications

References 119 publications

Closed equations of the two-point functions for tensorial group field theory

Closed equations of the two-point functions for tensorial group field theory

Group field theory and holographic tensor networks: dynamical corrections to the Ryu–Takayanagi formula

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

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