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Strings: Theory of Everything, Something, or Nothing? Robert N. Oerter.
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Transcript of Strings: Theory of Everything, Something, or Nothing? Robert N. Oerter.
Strings:
Theory of Everything, Something, or Nothing?
Robert N. Oerter
The Standard Model
Fermions
Family
1 2 3
Neutrinos νe νμ ντ
Electrons
& Kin
e μ τ
Quarks u, u, u c, c, c t, t, t
d, d, d s, s, s b, b, b
The Standard Model
Bosons
Gauge
Particles
W+, W- Dubya-plus,
Dubya-minus
Z0 Zee-zero
γ Photon
Symmetry
Breakers
H Higgs
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• ν mass << e mass << quark mass
• Dark Matter – not “normal matter”
• Dark Energy
• Gravity (General Relativity) left out
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?
Strings
Closed String Open String
Free Relativistic Point Particle
• Action
dmcS 2
Least action principle: minimize the invariant length of the world-line
Quantum Mechanics: sum over all paths
/iSePhase
Free Relativistic String
Xμ(σ)
X1
X3
X2
Four-vector Xμ = (X0, X1, X2 , X3)
X0 = ct
Free Relativistic String
World-sheet
String Action
(World-sheet area)S
2 2
2
T X XS d d
String Equations of Motion
2 2
2 20X
Classical string - solutions
022
LR XX
1cos[ ( ) ]o cm n nX x p a n
T
Constraints:
Each point on the string moves at the speed of light (for pure left- or right-mover)
Write X = XR(τ-σ) + XL(τ+σ)
The Quantum String
• Assign a phase to each world-sheet
• Sum over all 2-D surfaces Xμ(σ,τ)
• Feynman diagrams for particles:
/iSePhase
4( )freeS d x
4intS i d x
String Interactions
String Interactions
• No new parameters needed
• String theory smoothes out the interaction vertex
• All infinities of field theory are eliminated
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 = (2πT)n; n = 1, 2, 3, …
The Quantum String
• The Bad News– Tachyon: m2 = -2πT
– No fermions– Quantization requires D = 26 spacetime
dimensions
• Connection with General RelativityBackground spacetime
String quantization in a curved background General Relativity!
Superstrings
• Anti-commuting numbers: θ1θ2 = - θ2θ1
• Spacetime described by (Xμ, θα)
• Supersymmetric theory: fermion-boson symmetry• No Tachyons• Quantization requires D=10 spacetime coordinates
and 16 anticommuting coordinates
• Gauge groups SO(32), E8xE8
Xμ
θα
From 10-D to 4-DCompactification
• 6 of the dimensions are very small
• Topology determines the number of fermion families
• Shape determines coupling constants
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)
Non-Newtonian Gravity? (Adelberger & Eöt-wash)
Planck-scale physics?
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
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