# Creating 3, 4, 6 and 10-dimensional spacetime from W3 symmetry

## TL;DR

This paper proposes a model where breaking W3 symmetry in algebraic structures leads to the emergence of spacetime dimensions 3, 4, 6, and 10, connecting algebraic properties to fundamental universe dimensions.

## Contribution

It introduces a novel approach linking Jordan algebras and W3 symmetry breaking to the emergence of specific spacetime dimensions.

## Key findings

- Spacetime dimensions 3, 4, 6, and 10 arise from symmetry breaking.
- Jordan algebras of 3x3 Hermitian matrices underpin the model.
- Higher-dimensional universes are connected to algebraic structures.

## Abstract

We describe a model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four "magical" Jordan algebras of 3x3 Hermitian matrices with real, complex, quaternion and octonion entries, respectively. The simplest symmetry breaking leads to universes with spacetime dimensions 3, 4, 6, and 10.