Pith. sign in

REVIEW 4 cited by

$O(N)$ Random Tensor Models

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1512.06718 v2 pith:EKBGG7WC submitted 2015-12-21 math-ph hep-thmath.MP

Sylvain Carrozza , Adrian Tanasa This is my paper · ORCID
classification math-phhep-thmath.MP
keywords modeltensorclassexpansiongraphsmodelscriticalexistence
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the $U(N)$ invariant models. We first exhibit the existence of a large $N$ expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large $N$ expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

  1. Melonic Dominance in Subchromatic Sextic Tensor Models

    hep-th 2019-08 conditional novelty 7.0 of 10

    Sextic tensor models with O(N)^r symmetry and r<5 have exactly three maximally-single-trace interaction vertices, and each yields a large N limit dominated by (generalized) melonic diagrams.

  2. Additional constraints for the tensor bootstrap

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    New positivity constraints from open bubbles and color matrices provide sharp bounds on unitary tensor integrals at finite N and probe deviations from Gaussian universality.

  3. Asymptotic safety meets tensor field theory: towards a new class of gravity-matter systems

    hep-th 2025-01 conditional novelty 6.0 of 10

    Adding asymptotically safe gravity to the O(N)^3 tensor field theory converts its asymptotic freedom into an interacting fixed point at a non-zero quartic coupling.

  4. Notes on Tensor Models and Tensor Field Theories

    hep-th 2019-07 unverdicted novelty 2.0 of 10

    Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.

Pith tools