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.
Highlights
String field theory is notoriously complicated, but the so-called noncritical string field theory [1,2,3] is a lot simpler
The starting point is the continuum limit of two-dimensional causal dynamical triangulations (CDT) [5], a limit which is two-dimensional Hořava–Lifshitz quantum gravity if spacetime topology is trivial [6]
Here we are interested in a generalized CDT where spacetime topology can change [7]
Summary
The Niels Bohr Institute, Copenhagen University Blegdamsvej 17, 2100 Copenhagen Ø, Denmark and Institute for Mathematics, Astrophysics and Particle Physics (IMAPP). Tokyo Institute of Technology Department of Physics, High Energy Theory Group 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan (Received April 10, 2017). We describe a CDT-like model where breaking of W (3) symmetry will lead to the emergence of time and, subsequently, of space. The simplest such models which lead to higher dimensional spacetimes are based on the four “magical” Jordan algebras of 3×3 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
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