Transcript Strings: Theory of Everything, Something, or Nothing? Robert N. Oerter The Standard Model Family Fermions Neutrinos νe νμ ντ Electrons e & Kin Quarks u, u, u μ τ c, c, c t, t, t s, s,

Strings:
Theory of Everything, Something,
or Nothing?
Robert N. Oerter
The Standard Model
Family
Fermions
1
2
3
Neutrinos νe
νμ
ντ
Electrons e
& Kin
Quarks
u, u, u
μ
τ
c, c, c
t, t, t
s, s, s
b, b, b
d, d, d
The Standard Model
Bosons
Gauge
Particles
Symmetry
Breakers
W+, W-
Dubya-plus,
Dubya-minus
Z0
Zee-zero
γ
Photon
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
S   mc
2
 d
Least action principle:
minimize the invariant length
of the world-line
Quantum Mechanics: sum over all paths
Phase e
iS / 
Free Relativistic String
X3

Four-vector Xμ = (X0, X1, X2 , X3)
Xμ(σ)
X0 = ct
X2
X1
Free Relativistic String


World-sheet
String Action
S  (World-sheet area)
 2
 2

T  X   X 
S   
 
 d d
2       


String Equations of Motion
2
 2
  
 2 X 0

2
 
 
Classical string - solutions
1 
X  xo 
pcm   an cos[n(   )  n ]
T


Constraints:
Write X = XR(τ-σ) + XL(τ+σ)
 X R   X L 

 
 0
     
2
2
 Each point on the string moves at the speed of
light (for pure left- or right-mover)
The Quantum String
• Assign a phase to each world-sheet
Phase e
iS / 
μ
• Sum over all 2-D surfaces X (σ,τ)
• Feynman diagrams for particles:

S free   (    )d x
4
Sint  i   d 4 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 Relativity
Background
spacetime
String quantization in a curved background  General Relativity!
Superstrings
• Anti-commuting numbers: θ1θ2 = - θ2θ1
• Spacetime described by (Xμ, θα)
θα
Xμ
• Supersymmetric theory: fermion-boson symmetry
• No Tachyons
• Quantization requires D=10 spacetime coordinates
and 16 anticommuting coordinates
• Gauge groups SO(32), E8xE8
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
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 Planckscale 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