Geometry in transition in four dimensions: A model of emergent geometry in the early universe and dark energy

TL;DR

This paper investigates a six matrix model exhibiting a phase transition from a fuzzy four-sphere geometry with dark energy-like fields at low temperature to a non-geometrical phase at high temperature, relevant for early universe and dark energy modeling.

Contribution

It introduces a six matrix model with $SO(3) imes SO(3)$ symmetry that dynamically generates a fuzzy four-sphere geometry and explores its phase transition properties.

Findings

Identifies a phase transition between geometrical and non-geometrical phases.

Shows the geometrical phase features a fuzzy four-sphere with weakly coupled gauge and scalar fields.

Demonstrates relevance to early universe geometry and dark energy phenomena.

Abstract

We study a six matrix model with global $SO(3)\times SO(3)$ symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. This is an exotic phase transition in the same universality class as the three matrix model but with important differences. The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy four-sphere background ${\bf S}^2_N\times{\bf S}^2_N$, with an Abelian gauge field which is very weakly coupled to two normal scalar fields playing the role of dark energy.