# CDT and the Big Bang

## TL;DR

This paper proposes a model where breaking W3 symmetry in a CDT-like framework leads to the emergence of spacetime dimensions, notably 3, 4, 6, and 10, based on Jordan algebras.

## Contribution

It introduces a novel approach linking Jordan algebras to spacetime emergence through symmetry breaking in a CDT-like model.

## Key findings

- Higher-dimensional spacetimes emerge from symmetry breaking.
- The model connects Jordan algebras to spacetime dimensionality.
- Universes with dimensions 3, 4, 6, and 10 are derived.

## Abstract

We describe a CDT-like 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.