Melonic phase transition in group field theory

Aristide Baratin; Daniele Oriti; James P. Ryan; Matteo Smerlak; Sylvain Carrozza

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Melonic phase transition in group field theory

Aristide Baratin, Sylvain Carrozza, Daniele Oriti, James P. Ryan, Matteo Smerlak

High Energy Physics - Theory · Submitted 18 Jul 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes.

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arXiv ID1307.5026 (version 2)

Pith ID3DR7NUD5, Pith's permanent record of this paper and its review

CitationAristide Baratin, Daniele Oriti, James P. Ryan, Matteo Smerlak, Sylvain Carrozza. "Melonic phase transition in group field theory." arXiv:1307.5026 (2013). https://pith.science/paper/3DR7NUD5

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.41 · compares with prior results 0.16 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres.	background 1.00	0.06	0.06	asserted 1.00
s1	In this note, we deepen the analysis of this melonic sector.	contribution 0.94	0.63	0.03	asserted 0.55
s2	We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem.	result 0.59	0.96	0.13	asserted 1.00
s3	Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes.	result 0.99	0.92	0.68	asserted 1.00
s4	We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity.	limitation 0.81	0.30	0.03	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity.

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References

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
hep-th 2014-11 conditional novelty 6.0 of 10

The first functional renormalisation group treatment of tensorial group field theory yields explicit beta functions for a rank-3 model, a non-autonomous flow traced to the group-manifold radius, and Gaussian plus non-...
Discrete Renormalization Group for SU(2) Tensorial Group Field Theory
hep-th 2014-07 conditional novelty 6.0 of 10

Within a truncated four-coupling continuous flow, the rank-3 SU(2) tensorial group field theory is not asymptotically free for positive marginal couplings, contrary to prior expectation.
Functional Renormalisation Group analysis of Tensorial Group Field Theories on $\mathbb{R}^d$
hep-th 2016-01 conditional novelty 5.0 of 10

Truncated FRG flows of rank-d TGFTs on R, with and without gauge invariance, show asymptotic freedom in the UV and non-Gaussian IR fixed points consistent with a condensation-type phase transition.
Group field theory as the 2nd quantization of Loop Quantum Gravity
gr-qc 2013-10 conditional novelty 5.0 of 10

Second-quantizing loop quantum gravity's spin networks yields group field theory, giving a general map from canonical quantum dynamics to a specific group field theory model.
The continuum limit of loop quantum gravity - a framework for solving the theory
gr-qc 2014-09 accept novelty 3.0 of 10

The paper argues that the continuum limit of loop quantum gravity is equivalent to the physical Hilbert space and sketches an iterative coarse-graining program, with diffeomorphism symmetry as the indicator that the l...

Show 3 more citing papers

Invitation to Random Tensors
hep-th 2016-09 accept novelty 2.0 of 10

Random tensors extend random matrix models to higher dimensions, and a 1/N expansion indexed by a new invariant called the degree turned a stalled program into a working theory of random D-dimensional spaces.
Flowing in Group Field Theory Space: a Review
gr-qc 2016-03 accept novelty 2.0 of 10

Tensor-invariant bubble interactions supply group field theories with enough locality to renormalize, yielding a classified table of power-counting renormalizable models and hints of Wilson-Fisher-like fixed points.
Group Field Theory and Loop Quantum Gravity
gr-qc 2014-08 accept novelty 2.0 of 10

Group field theory reformulates loop quantum gravity as a quantum field theory of spin network vertices, giving spin foam models a generating functional and a route to continuum and cosmological limits.

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26 arXiv papers cite this in 28 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 19 sentences without a confident label

Cites it as background 9 papers

The properties of these divergences have been studied in the context of the Ponzano-Regge model of 3d quantum gravity and discrete BF theory [ref] , group field theory [ref] and EPRL model: with both Euclidean [ref] and Lorentzian signature [ref] .

Infrared divergences in the EPRL-FK Spin Foam model · Introduction · 0.97
The general structure has been studied in 3-d [ref] and also in 4-d topological group field theory [ref] .

Bulk amplitude and degree of divergence in 4d spin foams · Introduction · 0.83
Their leading order behaviour has been studied [ref] and some renormalizable GFT models [ref] have been introduced.

Weighting bubbles in group field theory · Introduction · 0.89

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