Line of fixed points in a bosonic tensor model

DOI10.1007/JHEP06(2019)053zbMATH Open1416.81113arXiv1903.03578OpenAlexW3103663212WikidataQ127669355 ScholiaQ127669355MaRDI QIDQ2314914

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Publication date: 30 July 2019

Published in: (Search for Journal in Brave)

Abstract: We consider the $O(N{)}^3$ tensor model of Klebanov and Tarnopolsky cite{Klebanov:2016xxf} in $d<4$ with a free covariance modified to fit the infrared conformal scaling. We study the renormalization group flow of the model using a Wilsonian approach valid in any $d$ (notably we do not require $d=4-epsilon$ with small $epsilon$). At large $N$, the tetrahedral coupling has a finite flow, hence it becomes a free parameter. The remaining flow can be parameterized by two couplings which do not mix. We show that, at leading order in $1/N$ but non perturbatively in the couplings, the beta functions stop at quadratic order in the pillow and double-trace couplings. We find four fixed points which depend parametrically on the tetrahedral coupling. For purely imaginary values of the latter we identify a real and emph{infrared attractive} fixed point. We remark that an imaginary tetrahedral coupling is in fact natural from the onset as the tetrahedral invariant does not have any positivity property, and moreover in the large-$N$ limit beta functions depend on the square of the tetrahedral coupling, thus they remain real, as long as the other couplings stay real.

Full work available at URL: https://arxiv.org/abs/1903.03578

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