Quantum Graphity

TL;DR

Quantum Graphity presents a background independent model where degrees of freedom on a complete graph exhibit a phase transition, leading to emergent low-dimensional geometry and potential cosmological implications.

Contribution

The paper introduces a novel background independent model with permutation symmetry, demonstrating emergent geometry and a cosmological transition.

Findings

Low energy phase exhibits emergent lattice structure

Permutation symmetry breaks to translation symmetry

Model suggests a universe transition avoiding the horizon problem

Abstract

We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in which physics on a low dimensional lattice emerges and the permutation symmetry is broken to the translation group of that lattice. In the high temperature, or disordered, phase the permutation symmetry is respected and the average distance between degrees of freedom is small. This may serve as a tractable model for the emergence of classical geometry in background independent models of spacetime. We use this model to argue for a cosmological scenario in which the universe underwent a transition from the high to the low temperature phase, thus avoiding the horizon problem.