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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/2101.04970v2 (pdf) |
| Date accepted: | 2021-08-26 |
| Date submitted: | 2021-07-16 10:44 |
| Submitted by: | Vignes-Tourneret, Fabien |
| Submitted to: | SciPost Physics Core |
| 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.
Author comments upon resubmission
List of changes
Apart from correcting the typos indicated by the referee, we added two paragraphs at the end of the introduction (see p. 4) to precise what means the constructive program about the T^4_5 model and what are its first next steps.
The referee also suggested we add some explanations about how tensor models generate tensor graphs and about the graphical expansion in the intermediate field representation. This in fact is nothing but the very standard procedure of deriving Feynman graph expansions from a quantum field theory action. Moreover we think that our paper cannot easily be made accessible to readers who do not know enough QFT. Even if we would have added explanations about the different Feynman graph expansions used in the manuscript, readers who do not know QFT enough would have been unable to understand the renormalization parts (Sections 3 and 4). This is why we did not add any other explanations about tensor and intermediate field Feynman graphs.
Published as SciPost Phys. Core 4, 029 (2021)