Lectures on String Theory

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Lectures on String Theory
Music of the Spheres
Jan Pieter van der Schaar
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Outline of the series

• Why do we need string theory
• What is string theory
• Latest developments

stands for Mystery

• Approximate nature of string theory
• D-branes and black holes
• Dualities and M-theory

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Summary last week

• String vibration modes correspond to particles
• Strings require ten space-time dimensions
• Our understanding is only approximate

• Heterotic SO(32) closed superstrings
• Heterotic E8 x E8 closed superstrings
• Type I open and closed superstrings
• Type IIA closed superstrings
• Type IIB closed superstrings

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Interacting strings

• Only approximately known through tube diagrams
• Strength of interactions determined by the string
  coupling and only when this number is smaller
  than 1 can we use our approximate description in
  terms of tube diagrams
• Strong string interactions roughly correspond to
  strong gravity, in which case the tube diagram
  approximation is no longer under control

Many interesting questions we would like to
answer involve strong string coupling at some
point, for instance selecting the space-time
stage, understanding black holes etc.
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1/16
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gs2
gs4
gs6
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String theory vs. quantum field theory
From QFT we can deduce the consecutive series of
approximations in terms of Feynman diagrams, but
in principle we can study (some aspects of)
strongly coupled QFT
QFT


String theory only defined in terms of tube
diagrams providing us with a consecutive series
of approximations
String Theory
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Superstrings and the correspondence principle

• If the length scales under consideration are much
  larger than the string length a point-particle
  description should be a good approximation
• At low energies we therefore approximately obtain
  supersymmetric quantum field theories including
  gravity supergravity

Superstrings
Supergravity
string length corrections
10-33 cm
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Introducing D-branes

• D stands for Dirichlet a mathematician
• A surface on which open strings end Dirichlet
  boundary conditions
• Think of it as an open string soap-bubble
  (membrane)
• Embedded in a closed string theory
• They have charge Q, mass M and p extended
  directions
• No force between N parallel D-branes !
• We can use our string tube diagram
  approximation when gravity is weak, so when the
  mass M of the D-brane is small

J. Polchinski
M,Q
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Black hole physics

• Created when nothing can stop the gravitational
  attraction
• Space-time singularity, black hole horizon
  surrounding the no escape zone (Schwarzschild
  radius)
• Elementary particles uncertainty in position is
  usually larger than its Schwarzschild radius
• No longer true when Planck scale energies are
  involved!
• Black holes have mass, charge and can rotate, but
  thats it

Sun 3 km Electron 10-55 cm
J. Wheeler Black holes have no hair
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Black hole quantum physics
S. Hawking

• Black holes emit black body Hawking radiation
  (tiny)
• Can be assigned a temperature and entropy
• Entropy is a measure of disorder or randomness
• We lack a microscopic understanding

BH (Sun) TH 0.00000001 K BH (Electron) TH
1052 K Entropy BH (Sun) 1077 Entropy Universe
1094
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Black p-brane solutions

• Extended generalizations of black hole solutions
• Classical solutions of supergravity General
  Relativity plus generalized electromagnetic
  fields
• Sources have a mass M, a charge Q and p extended
  directions (p0 black hole) heavy objects
• What do they correspond to in string theory?

Also known as Pea brains
Point-particle 0-brane
String 1-brane
Membrane 2-brane
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From D-branes to black holes

• D-brane picture valid at weak gravitational
  coupling small of D-branes
• A black hole appears at strong gravitational
  coupling large of D-branes
• Understanding of black holes in terms of D-branes
  and open strings!

Q, M
Q, M
Suggests that the information loss problem is a
result of our incomplete understanding of black
holes in the D-brane picture there is no problem!
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String dualities

• Strings are very useful objects to consider at
  weak coupling
• We like strings because they can deal with
  graviton exchange
• Degrees of freedom can change e.g. consider
  water and ice
• Something similar happens in string theory at
  strong coupling new (weakly coupled) degrees of
  freedom can be used in an approximate description
• This phenomenon is generally called a duality
• Particle/wave duality
• Strong/weak coupling duality (electric/magnetic)

E. Witten
A dream come true!
Second Superstring Revolution (1995)
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The hidden eleventh dimension

• Highest dimension for supergravity theories
• Gives a ten-dimensional supergravity (IIA) when
  wrapped on a circle and the radius turns out to
  be related to the string coupling !
• Small string coupling 10 dimensions
• Strong string coupling 11 dimensions
• Strings turn into Membranes

M. Duff P.K. Townsend E. Bergshoeff E.
Sezgin
Membrane
String
gs
D11 SUGRA
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What is M-theory?

• Membrane, Mystery, Mother, Magic,

WE DO NOT KNOW!
Membranes
Eleven dimensions
String theory
P-branes
P.K. Townsend Pea brain democracy!
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What about experiments?
Principle of Science the test of all knowledge
is experiment

• Never say never, we are working on it
• One ongoing single big experiment is very
  promising (in my humble opinion)

Our universe
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Summary of todays lecture

• String theory, using D-branes, has given us some
  clues about the constituents of some black holes
• Five superstring theories are approximate corners
  of a more fundamental structure called M-theory
• We do not yet know what M-theory is
• Involves membranes, eleven dimensions and more

E. Witten Understanding what M- theory really
is would transform our understanding of nature at
least as radically as occurred in any of the
major scientific upheavals in the past
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Credits

• The internet in general, but in particular
• www.particleadventure.org
• www.superstringtheory.com
• The highly recommended book
• The Elegant Universe by Brian Greene
• The SMP crew
• David Gerdes, Carol Rabuck
• Demos Angela Plagemann, Mark Kennedy, Warren
  Smith
• Sponsor
• Dr. M. Lois Tiffany

Thanks Everybody!