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Can we make sense out of "Tensor Field Theory"?
by Vincent Rivasseau, Fabien Vignes-Tourneret
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Submission summary
| Authors (as registered SciPost users): | Fabien Vignes-Tourneret |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2101.04970v1 (pdf) |
| Date submitted: | 2021-02-25 13:48 |
| Submitted by: | Vignes-Tourneret, Fabien |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We continue the constructive program about tensor field theory through the next natural model, namely the rank five tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on $U(1)^5$. We make a first step towards its construction by establishing its power counting, identifiying the divergent graphs and performing a careful study of (a slight modification of) its RG flow. Thus we give strong evidence that this just renormalizable tensor field theory is non perturbatively asymptotically free.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2021-6-13 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2101.04970v1, delivered 2021-06-13, doi: 10.21468/SciPost.Report.3056
Strengths
1) Opens a new pathway in an existing or a new research direction, with clear potential for multipronged follow-up work: The T_5^4 model seems like a particularly interesting model to understand as it is asymptotically free and just renormalizable and in many ways seems far more accessible than non-Abelian gauge theories - the paper carries out several important first steps in rigorously constructing this model in the context of constructive field theory
2) Provides a novel and synergetic link between different research areas - This investigation of the T_5^4 model is likely accessible to a much wider audience than the random tensor community, such as the wider constructive field theory community and also perhaps the stochastic analysis community
Weaknesses
1) As the paper progresses, it becomes much less accessible to readers unfamiliar with [Riv91], random tensor models, and intermediate field methods
Report
I believe the article under review meets the journal's acceptance criteria and I strong recommend it for acceptance with minor revisions. The paper begins the analysis of a very interesting model and presents its features in a way that is more accessible than most papers on similar topics. The technical level is good and it is carefully written.
In addition to a few minor typos listed below, I also make some suggestions about changes that I believe would help make the paper easier to follow for those in other areas (such as stochastic quantization). While making the paper self-contained is not a reasonable aim, some additional material on what it means to construct a model like this, ribbon graphs, and/or intermediate field maps would help make things more accessible to a wider audience but aren't essential for the paper being published.
Requested changes
Minor points
1) Second paragraph of Introduction - "electroweek" should be "electroweak"
2) Section 1.3, "To explicit the interaction (...).." should be "To make the interaction (...) explicit..."
3) The formula for the interaction at the bottom of page 5 should probably come with a sentence indicating what the sum over bold indices is
4) Pg 7, "c-deges" should be "c-edges"
Areas where some detail/exposition might makes things much easier for people in areas
1) It might be good, perhaps in the introduction, to describe a bit what the steps of a constructive program for this model could be
2) Towards the beginning of section 2, a computation showing how one generates stranded graphs in perturbation theory
3) Section 2.3 could give a bit more detail on the graphical expansion with intermediate fields