The causal matrix model Willem Westra and Stefan Zohren Leipzig

What and Why? Two dimensional quantum gravity Non critical (bosonic) string theory = Strings living in target space with D≠26 Toy model for 4d quantum gravity

Two different theories? Euclidean 2D quantum gravity Current Worldsheet definition of (non critical) string theory Causal 2D quantum gravity Toy model for 4d causal quantum gravity

Causal 2D quantum gravity Toy model for 4d causal quantum gravity Euclidean 2D quantum gravity Current Worldsheet definition of (non critical) string theory Our new insight

Two different theories?? Euclidean quantum gravity Conformal field theory (CFT): Conformal gauge Liouville theory Euclidean dynamical triangulations (EDT) Matrix models Loop equations Saddle point methods Orthogonal polynomials Causal quantum gravity ?? Propertime gauge Quantum mechanics Causal dynamical triangulations (CDT) Transfer matrix Continuum formulation Discrete formulation Technology

The big stuff: Gravity Einstein’s theory of general relativity, 1918

Gravity: curvature of space-time Matter curves space-time Curved space-time tells matter how to move Gravity = Geometry

The small: Quantum mechanics Schrödinger’s equation, 1927

Quantum Mechanics Everything that can happen... does happen What we see is the stuff that is most probable to happen

big + small gravity + quantum curved space-time + probability

Curved space + quantum Task: count all possible curved space-times Compute the most probable ones Solution: build space time from little “Lego blocks” Count the number of ways the Lego blocks can be put together

1+1 dimensional space times One dimension of space One dimension of time Simplest Lego blocks: triangles Task: count the number of ways one can glue triangles together

Counting the triangles N NN

N N+1

An example

Splitting the universe N N+1 N

The standard equation N N+1 N

Missing a move? N N+1 N