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

Sylvain Carrozza (1, 2) , Daniele Oriti (2) , Vincent Rivasseau (1, 3)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 AEI - Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
3 Perimeter Institute

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 tensorial interactions up to degree 6 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.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau. Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions. 2013. ⟨hal-00807833⟩