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

### Submission summary

 As Contributors: Fabien Vignes-Tourneret Arxiv Link: https://arxiv.org/abs/2101.04970v1 (pdf) Date submitted: 2021-02-25 13:48 Submitted by: Vignes-Tourneret, Fabien Submitted to: SciPost Physics 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:
Editor-in-charge assigned