Linearized group field theory and power-counting theorems

Joseph Ben Geloun (1, 2) , Thomas Krajewski (3, 1) , Jacques Magnen (4) , Vincent Rivasseau (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 ICMPA-Unesco Chair - International Chair on Mathematical Physics and Applications ICMPA-Unesco Chair, UAC, Bénin
3 CPT - Centre de Physique Théorique - UMR 6207
4 CPHT - Centre de Physique Théorique [Palaiseau]

We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We prove exact power counting theorems for any graph of such models. For linearized colored models the power counting of any amplitude is further computed in term of the homology of the graph. An exact power counting theorem is also established for a particular class of graphs of the nonlinearized models, which satisfy a planarity condition. Examples and connections with previous results are discussed.

Mots clés: perturbative study; renormalization

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Joseph Ben Geloun, Thomas Krajewski, Jacques Magnen, Vincent Rivasseau. Linearized group field theory and power-counting theorems. Classical and Quantum Gravity, 2010, 27 (15), pp.155012. ⟨10.1088/0264-9381/27/15/155012⟩. ⟨hal-00613874⟩