Tensorial methods and renormalization in Group Field Theories
Abstract
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 spacetime, 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 welldefined (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 cutoff expansion of the colored BoulatovOoguri models allow to explore further a nonperturbative regime in which infinitely many degrees of freedom contribute. The second set of results provide a new rigorous framework for the renormalization of socalled Tensorial GFTs (TGFTs) with gauge invariance condition. In particular, a nontrivial 3d TGFT with gauge group SU(2) is proven justrenormalizable at the perturbative level, hence opening the way to applications of the formalism to (3d Euclidean) quantum gravity.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.3736
 Bibcode:
 2013arXiv1310.3736C
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 PhD thesis, 229 pages, many figures. Partly based on arXiv:1104.5158, arXiv:1203.5082, arXiv:1207.6734 and arXiv:1303.6772