Abstract

Group field theory (GFT) is a second quantized reformulation of Loop Quantum Gravity and, at the same time, a generalization of matrix models for 2d gravity and lattice gravity path integrals.

In the first part of the talk, we give an introduction to the basic features of the GFT formalism, mainly from the point of view of simplicial geometry. We discuss the nature of the proposed fundamental degrees of freedom of spacetime, and of their quantum dynamics, and give an overview of recent results and research directions. We also emphasize the strict relation with canonical Loop Quantum Gravity, tensor models and lattice gravity path integrals.

In the second part of the talk, we show that effective cosmological equations for continuum homogeneous geometries can be derived directly from fundamental GFTs. The relevant quantum states are GFT condensates, and a form of nonlinear quantum cosmology arises as the hydrodynamics of the system, in the same way in which Gross-Pitaevskii equations arise from the quantum microscopic dynamics of real Bose condensates. A continuum spacetime emerges then from GFT as a quantum fluid, made of discrete pre-geometric building blocks.