2013/03/31 by Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau · 7 citations
Physics and Astronomy · #Asymptotic safety in quantum gravity #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Field (mathematics) #Gauge theory #Noncommutative and Quantum Gravity Theories #Point (geometry) #Quantum field theory #Quantum gravity #Renormalization #Renormalization group #gr-qc #hep-th
paper · pdf · doi:10.1007/s00220-014-1928-x
published as Commun. Math. Phys. 330, 581-637 (2014) · 51 pages, 15 figures, 2 tables. v2: minor corrections. v3: matches published version
openalex publication_date 2014/03/12 · arxiv created 2014/04/03 · arxiv updated 2014/07/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.