Line of fixed points in a bosonic tensor model

• Verfasst von: Benedetti, Dario [VerfasserIn]
• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Verfasst von: Harribey, Sabine [VerfasserIn]
• Titel: Line of fixed points in a bosonic tensor model
• Verf.angabe: Dario Benedetti, Razvan Gurau, and Sabine Harribey
• E-Jahr: 2019
• Jahr: 8 Mar 2019
• Umfang: 41 S.
• Fussnoten: Identifizierung der Ressource nach: Last revised 7 Jun 2019 ; Gesehen am 29.09.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2019
• Band/Heft Quelle: (2019), Artikel-ID 1903.03578, Seite 1-41
• DOI: doi:10.48550/arXiv.1903.03578
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: High Energy Physics - Theory
• Sach-SW: Mathematical Physics
• K10plus-PPN: 1804440280

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.