Duality, Spacetime and Quantum Mechanics

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Duality, Spacetime and Quantum Mechanics

• Robert de Mello Koch
• Center for Theoretical Physics

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• String theory is (at present) the most promising
  candidate for a theory of
• quantum gravity.
• It is a work in progress.

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• We have something very precise in mind when we
  use the words quantum and gravity.

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• When we talk about gravity, we mean general
  relativity, Einsteins theory of gravity. In
  Einsteins theory, gravity as a force is
  replaced by gravity as geometry.

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• What do we mean by geometry?
• Answer A recipe to measure lengths and
  angles.
• How can we replace forces by geometry?
• Answer Particles move on straight lines.
• What is a straight line between two points?
• Answer The shortest possible line between two
  points.

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• Einsteins theory gives us two pieces of
  information it tells us that
• Mass/energy curve spacetime
• Particles move on the shortest possible lines
  (geodesics)

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• So, now we know what we mean by the word
  gravity in the phrase quantum gravity. What
  do we mean by the word quantum?

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• Apart from gravity, we have three other forces in
  nature the electromagnetic, strong and weak
  nuclear forces. We use quantum field theory (the
  standard model) to describe these remaining three
  forces.

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• In classical physics, we are used to thinking
  that we can specify precisely where a particle is
  and how fast it is going. Further, if we can
  describe what forces act on our particle, we can
  say exactly where it will be at any instant in
  the future and exactly how fast it is going at
  that time.

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• In quantum theory, we cant simultaneously know
  where our particle is and how fast it is going.
  This is not because we are bad at experiments it
  is a statement about nature. We can only
  associate probabilities with given experimental
  outcomes.

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• Particles exchange gauge bosons (e.g. photons).
• The interaction occurs at well-defined place in
  spacetime.
• This fact implies UV (ultraviolet) divergences in
  Feynman diagrams.
• These divergences are fatal for gravity

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Draw pictures to represent physical processes
the pictures are a shorthand for mathematics.
Which physical processes are included? If its not
forbidden, its compulsory!
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• QFT gives expressions for
• Lines (types of particles particle masses
  their spin)
• Vertices (coupling strengths type of
  couplings)
• LOADS OF FREEDOM!

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• Its tough to unite general relativity and quantum
  field theory in a single framework. Is this a
  signal that we are doing something silly?

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In string theory we replace point like particles
by little loops
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Strings can sing

• At large distances the massless modes determine
  the physics. If we know what particles are in the
  theory, we know what forces are PREDICTED.
• Closed string GRAVITY
• Open string ELECTROMAGNETISM, STRONG AND WEAK
  NUCLEAR FORCE!

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• It is IMPOSSIBLE to include gravity in quantum
  field theory.
• Gravity is REQUIRED for string theory to make
  sense.

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How big is a string?

• Definitely lt 10-18m
• If we want to explain how weak gravity is
• L10-34m

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Mount Everest (8,850 m i.e.104m)
Proton 10-15m
closed string 10-34m
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For consistency, the tension of a fundamental
string is a constant this is not the case for
lumpy strings.
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• The hydrogen atom was very useful in developing
  quantum mechanics. Is there a hydrogen atom for
  quantum gravity?
• Yes black holes!

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D-brane solutions open strings end on the brane
closed string propagate in the bulk.
p-brane solutions closed strings near the brane
closed string propagate in the bulk.
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Many things agree

• same symmetries
• black hole entropy
• Hawking radiation/absorption

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Closed string or open string?
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The Maldacena conjecture
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IIB string theory on the background
Five-dimensional
Five-dimensional Anti de Sitter space
sphere

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is equivalent to super Yang-Mills theory!!

• The two theories live in a different number of
  dimensions
• One is a string theory and the other is a quantum
  field theory!
• Is this perhaps a way to inject experimental
  results into string theory? (We think so!)

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The energies match!

• Calculate the volume of the membrane (curvatures
  10 dimensional gravity classical)
• OR
• Calculate the energy in the wiggling ends of the
  open strings (flat space 4 dimensions no
  gravity quantum)

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• Comparison between energies and non-trivial
  excitations (dMK, Paulin-Campbell, Rodrigues)
• Tachyon condensation (dMK, Jevicki, Mihailescu,
  Tatar / dMK, Rodrigues)
• Non-commutative spacetimes (Cook, dMK, Murugan)
• Giant gravitons (dMK, Gwyn)
• Deformed conjectures with fewer symmetries (dMK,
  Murugan, Smolic2)