Tensorial methods and renormalization in Group Field Theories

Understand

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.