Geometry in transition: A model of emergent geometry

TL;DR

This paper investigates a three matrix model exhibiting a transition from a geometrical phase with gauge fields on a sphere to a non-geometrical phase, revealing complex critical phenomena and potential insights into the emergence of geometry in the universe.

Contribution

It introduces a novel matrix model demonstrating a transition with unique critical behavior and emergent geometry, providing a new perspective on how space might arise dynamically.

Findings

Discontinuous transition with divergent fluctuations

Emergent spherical geometry with gauge fields

Transition characterized by critical exponent α=1/2

Abstract

We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent $\alpha=1/2$. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early universe.