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arXiv · 1205.5513

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

Joseph Ben Geloun
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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 $ϕ^6$ ($ϕ^6_{(1/2)}$), $ϕ^4$ ($ϕ^4_{(1)}$) interactions and an anomalous term ($ϕ^4_{(2)}$). The $β$-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 $ϕ^6_{(1/2)}$ interactions whereas it is safe in the $ϕ^4_{(1)}$ sector. The remaining anomalous term turns out to possess a Landau ghost.

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Joseph Ben Geloun. 2012-10-07. Two and four-loop $β$-functions of rank 4 renormalizable tensor field theories. https://doi.org/10.1088/0264-9381%2F29%2F23%2F235011

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