Emergent 4D Quantum Geometry from Critical Space-Time Graphs

After a brief introduction to the problem of quantum gravity and the main solution approaches on the market I will focus on my new proposal of a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph. I will provide ample evidence that this simple network model has two critical points, an ultraviolet fixed point corresponding to fluctuating information bits and an infrared fixed point corresponding to an emergent geometric phase with space-time dimension 4. The model predicts that, at small scales, the space-time dimension decreases until space-time itself completely dissolves into a disordered soup of information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model and to illustrate the dimension decoupling mechanism I will solve a toy version of the model in the mean field approximation. At finite temperatures the universe graph emerges without big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no space-time inside and with “Schwarzschild-like” horizons with a lower spectral dimension.