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The causal matrix model
Willem Westra and Stefan Zohren
Leipzig 01 04 2008
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
Causal2D quantum gravity
Worldsheet definition of (non critical) string theory
Toy model for 4d causal quantum gravity
jl
Euclidean 2D quantum gravity
Causal2D quantum gravity
Worldsheet definition of (non critical) string theory
Toy model for 4d causal quantum gravity
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
QuickTime™ and a decompressor
are needed to see this picture.
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 N N
Counting the triangles
N N+1 N+1
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Splitting the universe
N N+1 N+1 N
The standard equation
N N+1 N
Missing a move?
N N+1 N
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