Group Field Theory: An overview
Laurent Freidel
TL;DR
The paper addresses constructing a background-independent quantum gravity dynamics and a meaningful physical inner product by leveraging Group Field Theory (GFT). It shows that GFT’s Feynman diagrams reproduce spin foam amplitudes and establishes a duality between GFT and local spin foam models, proposing a tree-level GFT two-point function as a triangulation-independent physical scalar product with a topology-summing extension controlled by a coupling $\lambda$. This framework positions GFT as a universal, third-quantized structure behind quantum gravity dynamics and connects the Wheeler-DeWitt-type constraints to GFT equations of motion. It further discusses non-perturbative aspects, including diffeomorphism symmetry and renormalization, and outlines key open challenges such as including matter and deriving the correct low-energy limit of general relativity.
Abstract
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that this theory leads to a natural proposal for the physical scalar product of quantum gravity. We also show in which sense this theory provides a third quantization point of view on quantum gravity.