Two and four-loop $\beta$-functions of rank 4 renormalizable tensor field theories

Abstract

A recent rank 4 tensor field model generating 4D simplicial manifolds has been proved to be renormalizable at all orders of perturbation theory [arXiv:1111.4997 [hep-th]]. The model is built out of ${\varphi }^6$ (${\varphi }_{(1/2)}^6$), ${\varphi }^4$ (${\varphi }_{(1)}^4$) interactions and an anomalous term (${\varphi }_{(2)}^4$). The $\beta$-functions of this model are evaluated at two and four loops. We find that the model is asymptotically free in the UV for both the main ${\varphi }_{(1/2)}^6$ interactions whereas it is safe in the ${\varphi }_{(1)}^4$ sector. The remaining anomalous term turns out to possess a Landau ghost.

31 pages, 31 figures; improved version

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