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 Carrozza
  • 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sylvain Carrozza
    • 1
    • 2
  • 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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