2013/10/14 by Sylvain Carrozza
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Asymptotic safety in quantum gravity #Black Holes and Theoretical Physics #Field (mathematics) #Field theory (psychology) #Focus (optics) #Functional renormalization group #Geometry #Group (periodic table) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Optics #Physics #Point (geometry) #Pure mathematics #Quantum #Quantum field theory #Quantum gravity #Quantum mechanics #Renormalization #Renormalization group #Theoretical physics #Thermal quantum field theory #Ultraviolet fixed point #gr-qc #hep-th
paper · pdf · doi:10.1007/978-3-319-05867-2
PhD thesis, 229 pages, many figures. Partly based on arXiv:1104.5158, arXiv:1203.5082, arXiv:1207.6734 and arXiv:1303.6772
arxiv created 2013/10/14 · openalex publication_date 2014/01/01 · arxiv updated 2014/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one hand, and to matrix models and tensor models on the other hand. They model quantum space-time, in the sense that their Feynman amplitudes label triangulations, which can be understood as transition amplitudes between LQG spin network states. The question of renormalizability is crucial if one wants to establish interesting GFTs as well-defined (perturbative) quantum field theories, and in a second step connect them to known infrared gravitational physics. Relying on recently developed tensorial tools, this thesis explores the GFT formalism in two complementary directions. First, new results on the large cut-off expansion of the colored Boulatov-Ooguri models allow to explore further a non-perturbative regime in which infinitely many degrees of freedom contribute. The second set of results provide a new rigorous framework for the renormalization of so-called Tensorial GFTs (TGFTs) with gauge invariance condition. In particular, a non-trivial 3d TGFT with gauge group SU(2) is proven just-renormalizable at the perturbative level, hence opening the way to applications of the formalism to (3d Euclidean) quantum gravity.