Next-to-leading order in the large $N$ expansion of the multi-orientable random tensor model

Adrian Tanasa; Matti Raasakka

RECORD

Next-to-leading order in the large $N$ expansion of the multi-orientable random tensor model

Matti Raasakka, Adrian Tanasa

High Energy Physics - Theory · Submitted 11 Oct 2013

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

The authors' main claim Furthermore, we find the radius of convergence and the susceptibility exponent of the NLO series for this model.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1310.3132 (version 2)

Pith IDFJVVNVC4, Pith's permanent record of this paper and its review

CitationAdrian Tanasa, Matti Raasakka. "Next-to-leading order in the large $N$ expansion of the multi-orientable random tensor model." arXiv:1310.3132 (2013). https://pith.science/paper/FJVVNVC4

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,229 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.29 · states limitation 0.67 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.39 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we analyze in detail the next-to-leading order (NLO) of the recently obtained large $N$ expansion for the multi-orientable (MO) tensor model. From a combinatorial point of view, we find the class of Feynman tensor graphs contributing to this order in the expansion. Each such NLO graph is characterized by the property that it contains a certain non-orientable ribbon subgraph (a non-orientable jacket). Furthermore, we find the radius of convergence and the susceptibility exponent of the NLO series for this model. These results represent a first step towards the larger goal of defining an appropriate double-scaling limit for the MO tensor model.

background contribution method result interpretation main claim

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	In this paper we analyze in detail the next-to-leading order (NLO) of the recently obtained large $N$ expansion for the multi-orientable (MO) tensor model.	contribution 0.98	0.90	0.08	asserted 0.96
s1	From a combinatorial point of view, we find the class of Feynman tensor graphs contributing to this order in the expansion.	contribution 0.73	0.96	0.08	asserted 1.00
s2	Each such NLO graph is characterized by the property that it contains a certain non-orientable ribbon subgraph (a non-orientable jacket).	result 0.96	0.86	0.14	asserted 1.00
s3	Furthermore, we find the radius of convergence and the susceptibility exponent of the NLO series for this model.	result 1.00	0.95	0.25	asserted 1.00
s4	These results represent a first step towards the larger goal of defining an appropriate double-scaling limit for the MO tensor model.	future work 0.93	0.31	0.14	asserted 0.95

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

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

In this paper we analyze in detail the next-to-leading order (NLO) of the recently obtained large $N$ expansion for the multi-orientable (MO) tensor model. From a combinatorial point of view, we find the class of Feynman tensor graphs contributing to this order in the expansion. Each such NLO graph is characterized by the property that it contains a certain non-orientable ribbon subgraph (a non-orientable jacket). Furthermore, we find the radius of convergence and the susceptibility exponent of the NLO series for this model. These results represent a first step towards the larger goal of defining an appropriate double-scaling limit for the MO tensor model.

Human review

How Pith checks papers → · Full audit of this paper →

References

How the literature uses it

6 arXiv papers cite this in 10 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 · 7 sentences without a confident label

Builds on it 1 paper

This analysis was extended to multi-orientable models in [ref] .

The Tensor Track, III · Single and Double Scaling · 0.87

Uses its method or tool 1 paper

Following [ref] , we compute in this subsection the radiuses of convergence and the susceptibility exponents of the leading and next-to-leading order series of the MO tensor model.

The Multi-Orientable Random Tensor Model, a Review · Leading and next-to-leading order series · 0.91

Cites it as background 1 paper

A number of efforts are currently being made in these directions [ref] .

Physical states in the canonical tensor model from the perspective of random tensor networks · Introduction · 0.82

What it cites · 27 sentences without a confident label

Uses the method or tool of 1 paper

Finally, we obtain from the Schwinger-Dyson equation [ref] 0 = ∫ϕ̅ ϕ δ/δϕ_ijk ( ϕ_i'j'k' e^-S[ϕ,ϕ̂] ) the relation G_NLO = 1 - 4λ^2 /λ^2 E_NLO relating the connected two-point function $G_NLO$ to the free energy $E_NLO$.

Towards a double-scaling limit for tensor models: probing sub-dominant orders · NLO series: radius of convergence & susceptibility · 0.88

Compares with 1 paper

It is worth noticing that in [ref] , the critical susceptibility for the NLO of the large $N$ expansion was found to be $3/2$, which is the same result as the one we obtained in the previous section (see equation [ref] above).

Towards a double-scaling limit for tensor models: probing sub-dominant orders · Perspectives — towards a double-scaling limit · 0.98

Cites as background 8 papers

The random variables described by the MO tensor model are a complex-valued rank-3 tensor $ϕ_ijk$ and its complex conjugate $ϕ_ijk$, where the indices take values in a range of integers $i,j,k=1,…,N$.[This generalizes naturally to different ranges for the different indices [ref] , but in this paper we will only consider tensors, whose indices take values in the same range.] The measure of the model consists of two parts: the Gaussian `kinetic' part and a non-Gaussian perturbation controlled by a parameter $λ∈R$.

The 1/N expansion of multi-orientable random tensor models · Definition of the model; large $N$ expansion · 0.89
In particular, for the case of colored tensor models, and originally the colored group field theory introduced in [ref] , the so-called color labels of the graph edges impose special restrictions on their Feynman graphs, so that much of the topological data is encoded into the labels.

Colored Group Field Theory · Introduction and motivation · 0.82
As already mentioned in the introduction, the double scaling limit of the colored [ref] and respectively “uncolored” [ref] IID tensor models have been implemented in [ref] and respectively [ref] .

Regular colored graphs of positive degree · Perspectives — towards a double-scaling limit · 0.99

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.