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

The Standard Model Fermions Family 123 Neutrinos νeνe νμνμ ντντ Electrons & Kin e μτ Quarksu, u, uc, c, ct, t, t d, d, ds, s, sb, b, b

The Standard Model Bosons Gauge Particles W +, W - Dubya-plus, Dubya-minus Z0Z0 Zee-zero γ Photon Symmetry Breakers HHiggs

Problems with the Standard Model Why three families? Why these particle masses? SM predicts mass of W ±, Z 0, 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 Least action principle: minimize the invariant length of the world-line Quantum Mechanics: sum over all paths

Free Relativistic String  X μ (σ) X1X1 X3X3 X2X2 Four-vector X μ = (X 0, X 1, X 2, X 3 ) X 0 = ct

Free Relativistic String World-sheet  

String Action String Equations of Motion

Classical string - solutions Constraints:  Each point on the string moves at the speed of light (for pure left- or right-mover) Write X = X R (τ-σ) + X L (τ+σ)

The Quantum String Assign a phase to each world-sheet Sum over all 2-D surfaces X μ (σ,τ) Feynman diagrams for particles:     

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: m 2 = (2πT)n; n = 1, 2, 3, …

The Quantum String The Bad News –Tachyon: m 2 = -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: θ 1 θ 2 = - θ 2 θ 1 Spacetime described by (X μ, θ α ) Supersymmetric theory: fermion-boson symmetry No Tachyons Quantization requires D=10 spacetime coordinates and 16 anticommuting coordinates Gauge groups SO(32), E 8 xE 8 XμXμ θαθα

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 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 ~ e 100 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