Renormalization of an Abelian tensor group field theory: solution at leading order

  • Vincent Lahoche
  • Daniele Oriti
  • Vincent Rivasseau
Open Access
Regular Article - Theoretical Physics

Abstract

We study a just-renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.

Keywords

Models of Quantum Gravity Renormalization Regularization and Renormalons 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Vincent Lahoche
    • 1
  • Daniele Oriti
    • 2
  • Vincent Rivasseau
    • 3
    • 4
  1. 1.LPT-UMR 8627, Université Paris 11Orsay CedexFrance
  2. 2.Max Planck Institute for Gravitational PhysicsAlbert Einstein InstitutePotsdamGermany
  3. 3.Laboratoire de physique théorique, UMR 8627, Université Paris 11Orsay CedexFrance
  4. 4.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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