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Communications in Mathematical Physics

, Volume 330, Issue 2, pp 581–637 | Cite as

Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions

  • Sylvain CarrozzaEmail author
  • Daniele Oriti
  • Vincent Rivasseau
Article

Abstract

We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that interactions up to ϕ 6-tensorial type are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.

Keywords

Quantum Gravity Heat Kernel Loop Quantum Gravity Tensor Model Spin Foam Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sylvain Carrozza
    • 1
    • 2
    Email author
  • Daniele Oriti
    • 2
  • Vincent Rivasseau
    • 1
    • 3
  1. 1.Laboratoire de Physique Théorique, CNRS UMR 8627Université Paris SudOrsay CedexFrance
  2. 2.Max Planck Institute for Gravitational Physics, Albert Einstein InstituteGolmGermany
  3. 3.Perimeter InstituteWaterlooCanada

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