Line of fixed points in a bosonic tensor model

  • Dario BenedettiEmail author
  • Razvan Gurau
  • Sabine Harribey
Open Access
Regular Article - Theoretical Physics


We consider the O(N)3 tensor model of Klebanov and Tarnopolsky [1] 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 − ϵ with small ϵ). 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 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 the beta functions depend on the square of the tetrahedral coupling, thus they remain real, as long as the other couplings stay real.


Renormalization Group 1/N Expansion Conformal Field Theory 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique (UMR 8627), CNRS, Univ.Paris-SudUniversité Paris-SaclayOrsayFrance
  2. 2.Centre de Physique Théorique (UMR 7644), CNRSÉcole PolytechniquePalaiseauFrance
  3. 3.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  4. 4.Ecole Normale Supérieure de LyonLyonFrance

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