Lecture 8: MTheory http:www'sukidog'comjpierrestringsmtheory'htm http:www'damtp'cam'ac'ukusergrpubli

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Lecture 8 M-Theoryhttp//www.sukidog.com/jpierre
/strings/mtheory.htmhttp//www.damtp.cam.ac.uk/us
er/gr/public/qg_ss.htmlhttp//www.lassp.cornel.ed
u/GraduateAdmissions/greene/greene.html
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M-theory
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Where M stands for

• The MOTHER of all theories
• Magic theory
• Matrix theory
• Membrane theory
• M is really an up-side-down W for Witten, after
  its discoverer in 1995.
• Or, as Witten himself suggested on the NOVA
  program, Murky theory because it is not well
  understood yet.

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M-Theory has actually had quite a media effect,
for example, Let M-theory records - rock your
universe!!
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5 string theories

• All theories share the same basic vibrational
  patterns. 10 spatial dimensions
• 6 curled up Calabi-Yau shapes
• They differ in how they incorporate
  super-symmetry as well as in the vibrational
  patterns they support.
• Vibrations along a string can travel in 2
  directions, clock- and anti-clockwise.
• Type IIA clock and anti-clockwise vibrations are
  exactly opposite in form (anti-particles)
• Type IIB clock and anti-clockwise vibrations are
  the same.

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5 stringy theories continued

• Each string theory has a coupling constant
• g. Weak coupling is when g lt1. When g is
  greater than or equal to 1 then there is strong
  coupling. 2 strings can collide and form a new
  excited state. This state can form 2 virtual
  strings and then reform back to 1 string and
  finally split apart. The probability of this
  virtual string formation (or loop formation) is
  determined by the coupling constant g.

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Vacuum quantum jitters cause loops of virtual
string pairs to form and subsequently recombine.
When glt1 additional loops become less likely to
occur. The processes become more likely when the
coupling constant g is greater than 1. When
more loops become increasingly likely,
perturbation theory fails.
The precise value of g impacts the mass, charge,
spin etc of the particles the strings
represent. We do not know how to calculate it.
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What are the String theories Out there ?

• Type I
• Type II A
• Type II B
• E8 x E8 Heterotic-E
• SO(32) Heterotic-O
• Super Gravity in 11 Dimensions
• Lets look at these one at a time

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Many different theories ?? http//www.sukidog.com
/jpierre/strings/susy.htm

• Type I SO(32)
• This contains open strings. It has one
  super-symmetry (N1) in 10 dimensions. Gauge is
  defined to be SO(32). The theory contains
  D-branes with 1,5 and 9 spatial dimensions.

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Summarized fromhttp//www.sukidog.com/jpierre/str
ings/susy.htm

• Type II A
• This is a theory of closed strings which has
  two (N2) super-symmetries in 10 dimensions. The
  2 gravitini (super partners of the graviton) move
  in opposite directions on the closed string world
  sheet and have opposite chiralities under the 10
  dimensional Lorentz group. It is a non-chiral
  theory. There is no gauge group. It contains
  D-branes with 0,2,4,6,8 spatial dimensions.
• Neveu-Schwarz fivebrane solitons present, not
  a D-branes, also known as NS fivebranes.

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Summarized fromhttp//www.sukidog.com/jpierre/str
ings/susy.htm

• Type II B
• This is also a closed string theory with N2
  super-symmetry. Here the 2 gravitini have the
  same chiralities under the 10 dimensional Lorentz
  group, so this is a chiral theory. No gauge
  group. It contains D-branes with -1,1,3,5,7
  spatial dimensions.
• Neveu-Schwarz fivebrane solitons present, not
  a D-branes, also known as NS fivebranes.

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Summarized fromhttp//www.sukidog.com/jpierre/str
ings/susy.htm

• Heterotic O
• This is a closed string theory with world
  sheet fields moving in 1direction on the world
  sheet which has a SUSY (super-symmetry) and
  fields moving in the opposite direction which
  have no SUSY. The result is N1 super-symmetry in
  10 dimensions. The non-SUSY fields contribute
  massless vector bosons to the spectrum which by
  anomaly cancellation are required to have an
  SO(32) gauge symmetry.

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Summarized fromhttp//www.sukidog.com/jpierre/str
ings/susy.htm

• Heterotic-E
• Historically the most promising. Closed string
  theory. This theory is identical to the SO(32)
  Heterotic-O string except that the gauge group is
  E8xE8 which is the only other gauge group allowed
  by anomaly cancellation.
• Heterotic theories (E O) do NOT contain
  soliton NS fivebranes or D-branes.

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Table of String Theorieshttp//www.sukidog.com/jp
ierre/strings
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Dualities ??http//www.sukidog.com/jpierre/string
s/duality.htm

• What does S-Dual mean ?
• What does T-Dual mean ?
• Ill explain each duality first and then say
  which theories are dual to each other.
• Physicists use the term dual to describe 2
  theories which may look different but
  never-the-less describe the same physics.
• Each string theory has its own coupling constant.

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T-Duality or R vs 1/R

• T-duality
• This duality related theories which are
  defined in a universe with dimension R to another
  which has dimension 1/R.
• Type IIA Type IIB string theories are
  related by T-duality, as are Heterotic-O
  Heterotic-E theories.

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As the coupling constant increases above
unity the string grows into a membrane. As the
coupling Is increased this string theory
resembles M-theory.
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Coupling constant becomes larger than unity A new
dimension opens up. M-theory is in 11 dim. This
shows that for large coupling this string
theory tends to M-theory.
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S-Duality (strong/weak coupling)

• S-Duality
• This duality relates the strong coupling limit
  of one theory to the weak coupling regime of
  another theory. Weak coupling can be calculated
  using perturbation theory, strong coupling
  cannot. (BPS states are used for strong coupling
  regimes.)
• Heterotic-O Type I string theories are
  related in this way. Type IIB string theory is
  self dual.

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Duality between theories
M-theory is described at low energy by 11 dim
super-gravity. This theory has membrane and
fivebranes as solitons but no strings.
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How does super-gravity fit in?

• Experiments do not have large enough energy to
  probe the ultra-small Planck length spatial
  dimensions of a string.
• We can approximate strings with point particles
  and use QFT in 10 dimensions. The QFT that most
  closely resembles string theory in this manner is
  10D super-gravity. The special properties of
  s-gravity discovered in the 70s and 80s are now
  understood to be the low energy forms of string
  theory.

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Super-gravity continued

• There are 4 different 10D s-gravities which
  differ in how SUSY is incorporated
• 3 of these resemble the low energy pt. particle
  forms of Type IIA, Type IIB and Heterotic-E
  string theories.
• The 4th gives the low energy form of Type 1 and
  Heterotic-O theories. This was the first hint
  that these two theories may be connected in some
  way!

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Overview Summary M-theory is still not
well Understood.
When the string theory coupling constant g is
small In any of the pointed outlying regions the
fundamental elements of the theory are 1D
strings. If you start at the Heterotic-E or Type
IIA regions and move Inward toward the center of
the M-theory map then the 1D Strings stretch
into 2D membranes.
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Strings, D-branes p-branes

• Physicist rely on supersymmetry to give an
  understanding of string theory beyond weak
  coupling. Properties of BPS states, are uniquely
  determined by SUSY and this allows us to
  understand their strong coupling characteristics.
• Work by Horowitz, Strominger and Polchinski
  has led to knowledge of what these strong coupled
  BPS states look like. 1D strings, 2D membranes,
  others are 3-branes, 4-branes and in general
  p-branes, 0ltplt9. Its not just strings anymore!

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Mass of these p-branes?

• Physicists have shown that the extended objects
  are inversely proportional to the string coupling
  constant.
• In the weak coupling regime of the 5 string
  theories, 1D strings are light particles but all
  other branes are very massive gtgt Planck mass.
  Since very large energy/mass particles are hard
  to create in an experiment, they are not seen.
• Branes have only a small influence in the 5 basic
  string theories. The effects of branes become
  important as you enter the center of the M-theory
  map, where the coupling constants increase.

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Coffee Break30 mins. of Wittens
talkhttp//online.kitp.ucsb.edu/online/plecture/w
itten/
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The End

• Lecture 9 Experimental Evidence
  in support of String theory.
• See you April 5th after the spring break.