Strings:

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Strings

• Theory of Everything, Something, or Nothing?
• Robert N. Oerter

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The Standard Model
Fermions Family Family Family Family
Fermions 1 2 3
Fermions Neutrinos ?e ?µ ?t
Fermions Electrons Kin e µ t
Fermions Quarks u, u, u c, c, c t, t, t
Fermions d, d, d s, s, s b, b, b
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The Standard Model
Bosons Gauge Particles W, W- Dubya-plus, Dubya-minus
Bosons Gauge Particles Z0 Zee-zero
Bosons Gauge Particles ? Photon
Bosons Symmetry Breakers H Higgs
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Problems with the Standard Model

• Why three families?
• Why these particle masses?
• SM predicts mass of W, Z0, and photon
• All other masses are arbitrary
• ? mass ltlt e mass ltlt quark mass
• Dark Matter not normal matter
• Dark Energy
• Gravity (General Relativity) left out

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Hints of New Structures

• Structure or Symmetry?
• Leptons built of still smaller preon particles?
• Grand Unified Theories (GUTs) what gauge group?
• Is a different kind of structure needed?

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Strings
Closed String
Open String
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Free Relativistic Point Particle

• Action

Least action principle minimize the invariant
length of the world-line
Quantum Mechanics sum over all paths
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Free Relativistic String
X3
?
Four-vector Xµ (X0, X1, X2 , X3) X0 ct
Xµ(s)
X2
X1
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Free Relativistic String
?
?
World-sheet
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String Action
String Equations of Motion
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Classical string - solutions
Constraints
Write X XR(t-s) XL(ts)
? Each point on the string moves at the speed of
light (for pure left- or right-mover)
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The Quantum String

• Assign a phase to each world-sheet
• Sum over all 2-D surfaces Xµ(s,t)
• Feynman diagrams for particles

?
?
?
?
?
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String Interactions
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String Interactions

• No new parameters needed
• String theory smoothes out the interaction
  vertex
• All infinities of field theory are eliminated

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The Quantum String

• Results of string quantization
• No infinities
• No additional coupling constants
• Massless particles
• Spin-0 scalar
• Spin-1 gauge boson
• Spin-2 graviton!!!
• Massive particles
• m2 (2pT)n n 1, 2, 3,

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The Quantum String

• The Bad News
• Tachyon m2 -2pT
• No fermions
• Quantization requires D 26 spacetime dimensions
• Connection with General Relativity

Background spacetime
String quantization in a curved background ?
General Relativity!
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Superstrings

• Anti-commuting numbers ?1?2 - ?2?1
• Spacetime described by (Xµ, ?a)
• Supersymmetric theory fermion-boson symmetry
• No Tachyons
• Quantization requires D10 spacetime coordinates
  and 16 anticommuting coordinates
• Gauge groups SO(32), E8xE8

?a
Xµ
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From 10-D to 4-D
Compactification

• 6 of the dimensions are very small
• Topology determines the number of fermion
  families
• Shape determines coupling constants

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Experimental Tests

• Large-mass relics of the Big Bang (not found)
• Fractional electric charges e/5, e/11 (not
  found)
• Departures from inverse-square law of gravity
  (Arkani-Hamed, et. al. - not found)
• Light from distant galaxies shows Planck-scale
  physics? (Ragazzoni et.al. - not found)

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Non-Newtonian Gravity? (Adelberger Eöt-wash)
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Planck-scale physics?
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The Goals of Physics

• Describing the world
• Make predictions
• Compact description
• Ease of use
• Theory of everything?
• Inconsistent equations are bad
• Maxwell / Newton ? Special Relativity
• Quantum Mechanics / General Relativity ? ?
• Would I know a TOE if it kicked me?
• Dark matter most of the mass in the universe!
• Can never access all regimes of size and energy

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Strings A TOE?

• Do strings describe the world?
• No longer a 1-parameter theory
• Actually a class of theories e100 of them!
• Not known how to choose between them
• No string predictions of masses, coupling
  constants
• No experimental prediction has been confirmed
• Not easy to use
• Do strings unify QM and GR?
• Graviton
• Derive (super)gravity for the background
  spacetime
• Black hole physics
• Strings A Theory of Something