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

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

Transcript of Strings: Theory of Everything, Something, or Nothing? Robert N. Oerter.

Page 1: Strings: Theory of Everything, Something, or Nothing? Robert N. Oerter.

Strings:

Theory of Everything, Something, or Nothing?

Robert N. Oerter

Page 2: 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

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The Standard Model

Bosons

Gauge

Particles

W+, W- Dubya-plus,

Dubya-minus

Z0 Zee-zero

γ Photon

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• ν mass << e mass << 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

dmcS 2

Least action principle: minimize the invariant length of the world-line

Quantum Mechanics: sum over all paths

/iSePhase

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Free Relativistic String

Xμ(σ)

X1

X3

X2

Four-vector Xμ = (X0, X1, X2 , X3)

X0 = ct

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Free Relativistic String

World-sheet

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String Action

(World-sheet area)S

2 2

2

T X XS d d

String Equations of Motion

2 2

2 20X

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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)

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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

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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 = (2πT)n; n = 1, 2, 3, …

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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!

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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

θα

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From 10-D to 4-DCompactification

• 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