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

A World Made of Strings

• String modes and particles
• Supersymmetry
• Strings and space-time

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Summary last week
String theory
E. Weinberg String theory is the only game in
town
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String theory vs. quantum field theory

• QFT predicts anti-particles
• Not very unique, many possible interactions can
  be introduced at interaction points
• Can not incorporate gravity (gravitons)

• String theory predicts (or postdicts)
• Gravity
• Gauge particles (photons, gluons)
• Supersymmetry
• Extra space-time dimensions
• Very unique, interactions are not arbitrary
• because they are described by the same string

g
g
Interaction point (vertex)
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String vibration modes

• Strings have to wiggle
• Classically to avoid collapse under its tension
• QM nothing can sit still
• Discrete spectrum of waves that fit
• Classically non-zero, positive energy
• QM vacuum energy can lead to negative or zero
  internal energy
• Different string modes correspond to particles
  with different properties!

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Determining the string length

• Among massless modes of a closed string
• The graviton particle!
• Tension of string has to be huge to describe the
  weakness of gravity
• Huge tension implies tiny string length Planck
  length 1.6 x 10-33 cm
• Second excited state masses are Planck mass
• A single string can vibrate in infinitely many
  ways infinite stair of particles with Planck
  mass steps

Planck mass 0.00001 grams
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String scales

• Proton mass 10-24 grams 1 GeV
• Electron mass 10-27 grams 0.5 MeV
• Planck mass 0.00001 grams 1019 GeV (kinetic
  energy of small airplane)

Mega 106 Giga 109 1 GeV 10-24 grams
TERRA INCOGNITA !
String scale
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Supersymmetry

• Matter (fermions) and forces (bosons) behave very
  differently
• Half integer spin ( ½ h ) are fermions and
  integer spin ( 1 h ) are bosons
• Quantum version of rotation, which is connected
  to rotational symmetry transformations
• Space-time symmetries can be uniquely extended
  with supersymmetries that connect fermions and
  bosons

S.N. Bose
Every fermion has a boson partner and vice versa
superpartners (compare to anti-particles)
E. Fermi
Fermions
Bosons
electron (1/2) selectron (0)
photon (1) photino (1/2)
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Supersymmetry has to be broken

• No superpartners have been observed
• High temperature or high energy supersymmetry
  would be restored
• Superpartner masses high but perhaps will be
  observed in the near future in accelerators

• Why theorists like supersymmetry
• Symmetry and elegance
• Solves some technical issues in Standard Model
  and Grand Unified Theories (GUT)

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Strings and supersymmetry
P. Ramond

• Bosonic string theory only contains boson
  particles
• Sure enough our world contains fermion particles
  (matterfermions, forcesbosons)
• Superstring theory
• Contains fermion particles
• Predicts supersymmetry !

A. Neveu
J. Schwarz
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Superstring theories
M. Green
J. Schwarz

• Ten space-time dimensions !
• Closed superstrings and closed open
  superstrings
• Different kinds of supersymmetries
• Five different superstring theories

First Superstring revolution (1984)
In principle a string theory only needs one input
parameter, the string tension, which is
determined by the strength of gravity
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Superstrings overview

• 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

Embarrassment of riches
E. Witten If one of the five theories describes
our universe, who lives in the other four worlds
?
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Extra space-time dimensions

• Obviously are universe is 4-dimensional time
  up/down left/right forward/backward
• However imagine our universe was 2-dimensional
  time left/right
• Now imagine that our world actually contains a
  small extra 3rd dimension that is curled up
• If the extra 3rd dimension is small enough
  2-dimensional observers will not be able to
  detect it !

Going back to our 4-dimensional universe we can
not exclude the possibility that our universe
contains small extra dimensions
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Signatures of extra dimensions

• Extra dimensions corrections to gravitational
  law
• Gravity at millimeter scales
• Current limit R lt 0.01 cm
• Particles can travel in the extra dimensions and
  because of the wavelike character of particles
  this motion in the extra dimensions is not
  arbitrary
• Kaluza-Klein modes with masses M 1/R
• Current limit R lt 10-18 cm

O. Klein
T. Kaluza
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Extra dimensions in string theory

• Amazingly, consistent quantum string theories can
  only be defined in a unique number of space-time
  dimensions !
• Superstrings require D10
• So six dimensions have to be curled up and very
  small
• The spectrum of particles of the string depends
  crucially on the shape and size of the extra 6
  dimensions
• Good news some of these look a lot like our
  world (Calabi-Yau)!

A. Strominger
P. Candelas E. Witten G. Horowitz
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Setting the stage in string theory

• General relativity tells us that the space-time
  stage is a treacherous swamp (space-time is
  dynamical)
• String theory includes quantum gravity
• Studying string theory (until recently) meant
  studying 2d tube string diagrams in a
  hand-picked, but not completely arbitrary,
  space-time stage (also called the string vacuum)
• Bad news possibilities to pick space-time stages
  seem to be endless and worse, without preference !

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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
• When the string coupling is strong we have no
  control not just quantitatively, but also
  qualitatively (until recently)

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.
gs2
gs4
gs6
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String signatures of extra dimensions

• Kaluza-Klein particles indicate extra dimensions
• Strings can wrap the compact extra dimensions
• Strings KK-tower and winding mode tower
• Minimal radius Rmin string length

5R
4R
3R
Rg0
Strings see space-time differently from the way
point-particles do
2R
R
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To summarize todays lecture

• String vibration modes correspond to particles
• To get fermions we need superstrings
• Superstrings predict supersymmetry
• Superstrings require 10 space-time dimensions
• Strings see space-time differently
• Our understanding is only approximate

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Come back next week

• Strongly coupled strings
• D-branes
• Black holes
• Dualities and M-theory

Anonymous It is all string theory to me