# Can we make sense out of "Tensor Field Theory"?

### Submission summary

 As Contributors: Fabien Vignes-Tourneret Arxiv 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 Academic field: Physics Specialties: Mathematical Physics 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:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics Core: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

We would like to thank the referee for her/his suggestions in order to improve and clarify the content of our manuscript. We also thank her/him for pointing out typos.

### 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.

### Submission & Refereeing History

Resubmission 2101.04970v2 on 16 July 2021
Submission 2101.04970v1 on 25 February 2021

## Reports on this Submission

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