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

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 ${\mathbf{S}}_N^2\times {\mathbf{S}}_N^2$, with an Abelian gauge field which is very weakly coupled to two normal scalar fields playing the role of dark energy.

arXiv comment5 pages, 6 figures

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Cited by in corpus (4)

• Quantum Gravity as a Multitrace Matrix Model
• Emergent fuzzy geometry and fuzzy physics in $4$ dimensions
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Wilsonian Matrix Renormalization Group