string theory: a status report · non-commutative geometry sometimes the space-time coordinates on...
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String Theory: A Status Report
N. Seiberg
Institute for Advanced Study
2004
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Foundations of Modern Physics
• Quantum Theory
• Special Relativity
• General Relativity
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Quantum Mechanics + Special Relativity
=
Quantum Field Theory
The standard model of particle physics
Unprecedented success!
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Adding Gravity/General Relativity
Many problems arise:
moon earth
graviton
graviton electron
Quantum fluctuations are infinite!
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Gravity = General Relativity
= Modification of space-time
This is not merely a technical problem
but a conceptual problem.
We should not expect the quantization to be easy.
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Conceptual problems:
• The light-cone undergoes quantum fluctuations
– How to maintain causality?
• Information loss in black holes(?)
– Is the theory unitary?
• The cosmological constant 10-120M4Planck
Why so small? Calculate it.
• Cosmology, early Universe, inflation
– Wave function of the Universe
– Initial conditions
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Challenge:
Combine General Relativity with
Quantum Mechanics
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String Theory
Invented in the late 60’s as a theory of the strong
interactions.
Mid 70’s: String theory is a theory of
gravity!
Gravity is not an option in string theory.
It is a logical consequence of it!
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Main idea: the fundamental building blocks
are not point-like particles but strings
Their small size (10-33cm) makes them look point-like.
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Different vibration modes of the string
are different particles.
electron quark
Very economical!
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The theory on the two-
dimensional string world-sheet
is reparametrization invariant
(geometrical).
String Interaction
Joining and splitting
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First String Revolution
The Perturbative era (Mid 80’s - Mid 90’s)
• Consistent perturbation expansion
• Several consistent string theories (type I, type IIA,
type IIB, heterotic SO(32), heterotic E8xE8)
• String propagation in curved spaces
Connection to conformal field theory
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• The theory has many ground states
characterized by the six dimensional
compactification.
• Some of these ground states are similar to
our world (4 dimensions, electrons,
photons, etc.).
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Experimental verification is not easy
In order to see stringy phenomena we need a
microscope with a resolution of 10-33cm.
The resolution of the best available accelerators is
only 10-16cm.
Indirect experimental confirmation is needed!
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Second String Revolution
The Non-perturbative era (Mid 90’s - ?)
• Exact results using the magic of supersymmetry
• Extended objects
• Large extra dimensions
• Non-commutative geometry
• String duality
• String theory is unique
• Black hole information puzzle
• Many “ground states”
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p-branes: 0-brane = particle
1-brane = string
2-brane = membrane
etc.
The theory has extended objects like membranes
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Some of them are regions where strings can end:
D-branes (Dirichlet branes)
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Non-Commutative Geometry
Sometimes the space-time coordinates on the
D-brane do not commute
[ x , y ] 0
(Like electrons in the first Landau level.)
New connections to mathematics.
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Extra Dimensions
In addition to the three space dimensions
there can be more “invisible dimensions”
• Small “invisible dimensions” (Kaluza Klein)
• Large “invisible dimensions” (brane world)
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Large “invisible dimensions” –
brane world
Our four space-time dimensions
We are trapped in a brane and cannot
“see” the other dimensions.
Gravity is weak because the extra dimensions
are large.
Extra
dimensions
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String Duality: The underlying space-time on which the
strings propagate is ambiguous
We cannot tell whether strings propagate on
or
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This duality generalizes:
• E B duality in electromagnetism
• P Q “duality” in quantum mechanics
• Order disorder duality in Ising model
Telling the same story in different languages.
Duality exchanges
strong coupling weak coupling
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All p-branes are equally fundamental.
String theory is not a theory of strings!
String duality exchanges the different branes
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Map of the ground states of
string theory
type I
type IIA
type IIB
heterotic E8xE8
heterotic SO(32)
11 dim. ground state We are here
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All previously known theories are now
understood as different descriptions of
the same theory.
String duality exchanges them.
Telling the same story in different languages.
The theory is unique!
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Some details
• “Fundamental objects” at one end are
composites elsewhere
• Weak coupling at one end corresponds to
strong coupling at another end
• The extrapolation from end to end uses the
magic of supersymmetry
• The theory is inherently quantum mechanical
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Black hole information puzzle
Suggestion: All the information about the
interior of a black hole is summarized by the
state of its surface, the horizon.
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Recent developments - Holography - show that in
string theory (at least in certain situations) the state of
the system is completely characterized by the behavior
of its boundary.
Strings in AdS = CFT on boundary
Entropy = Area
No information loss in black holes
=
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The Ground State(s)
The recent advances have uncovered many new
solutions of the equations of motion – ground states
• Is the ground state selected by initial conditions –
connection to cosmology?
• If all these solutions are acceptable, do they exist
elsewhere in the Universe – Anthropic solution?
• Our understanding lacks a crucial ingredient.
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Summary
• String theory is the only candidate for a complete theory of Nature.
• Ultimate confirmation of the theory will require verification by experiment.
• Its fundamental principles are not yet understood, but the past few years have seen tremendous progress:
- Nonperturbative understanding
- The theory is unique
- Black holes
- Connections with other branches of physics and mathematics