String Theory Gravity and Particle Physics Augusto Sagnotti

String Theory, Gravity and Particle Physics Augusto Sagnotti Scuola Normale Superiore & INFN, Pisa Astronomi. Amo, 23 -4 -2020

“Fundamental” Interactions KEY: ONLY SOME FORCES ARE «FUNDAMENTAL» • FRICTION: VERY IMPORTANT but NOT FUNDAMENTAL • GRAVITY: YES! BUT there is more: TERRESTRIAL = CELESTIAL A. Sagnotti – Astronomi. Amo, 23. 4. 2020 2

Particles and Field Theory 1. All matter is (apparently) made of “elementary” particles • Ordinary matter: electrons, protons, neutrons 2. Particles exert mutual forces • Example: Coulomb force 3. A charged particle creates an Electric Field : • • • Elegant dynamics: Maxwell equations and waves Embodies Special Relativity Problem: self-interaction and self-energy A. Sagnotti – Astronomi. Amo, 23. 4. 2020 3

Quantum Mechanics Classical Physics fails with key phenomena: • COLOR of HOT bodies • SPECIFIC HEAT of crystals • INTERACTIONS between light and matter • STRUCTURE and stability of ATOMS QUANTUM MECHANICS • NO DETERMINISM (in measurement) : wavefunction • Particle-wave duality & Uncertainty principle A. Sagnotti – Astronomi. Amo, 23. 4. 2020 4

Quantum Mechanics and Special Relativity Particles are waves (and waves are particles) Identical particles: bosons and fermions Special Relativity: ΔE > mc 2 can destroy a particle, transforming it into others Thus (m >0): (Compton wavelength) “Quantum Size” A theory of all types of (anti) particles ! A. Sagnotti – Astronomi. Amo, 23. 4. 2020 5

Quantum Field Theory: particles as quanta of wave fields • Example: photons and the e. m. field • Quantize the (bosonic) oscillators: A. Sagnotti – Astronomi. Amo, 23. 4. 2020 6

Quantum Field Theory • Bosons have positive zero-point energy • Fermions: Pauli principle and negative zero-point energy Supersymmetry (SUSY) : zero-point energies cancel for bosons and fermions of same mass A. Sagnotti – Astronomi. Amo, 23. 4. 2020 7

Particle Interactions QED: e. m. interactions of photons, electrons, and positrons, of “strength” Weak Interactions: Fermi (1933) Standard Model (1967) A. Sagnotti – Astronomi. Amo, 23. 4. 2020 8

The Standard Model Grounds: Quantum Mechanics & Special Relativity Compendium of what we know about Elementary Particles & their Interactions: • E. M. Interactions (photon ): QED • Weak Interactions: (W +, W -, Z 0) • Strong Interactions (8 gluons): QCD Weak and Strong: short “range” ! GRAVITY: waves graviton BUT: forces too strong at high energies ! A. Sagnotti – Astronomi. Amo, 23. 4. 2020 9

Gravity • Newton vs Coulomb : • Analogy with QED: Einstein: dynamics vs geometry gmn • MASS (energy) induces space-time CURVATURE v Graviton: gmn = mn + hmn (Vacuum energy: cosmological constant ! ) A. Sagnotti – Astronomi. Amo, 23. 4. 2020 10

Strong Interactions, Hadrons & QCD “Color Interactions compress “Faraday” lines Quarks: confined inside “color-neutral” hadrons STRING THEORY: from modeling an “infinitely thin” flux tube (Veneziano, 1968) BUT: 1. Unstable system 2. Extra dimensions (D=26!) A. Sagnotti – Astronomi. Amo, 23. 4. 2020 11

Strings & Gravity “Dilute” gravity on strings softer at high energies • Diluting energy on a scale ls “soft” gravity Elementary particles as string modes? A. Sagnotti – Astronomi. Amo, 23. 4. 2020 12

Strings & Particles Naively: normal modes > 0 particle masses > 0. NOT HERE! Zero-point fluctuations long-range forces! E. M, QCD, gravity: from subtle vacuum effect ! GRAVITY: inevitable ! A. Sagnotti – Astronomi. Amo, 23. 4. 2020 13

Superstrings What types of strings ? OPEN and CLOSED SUPERSTRINGS: • • BOSE and FERMI particles STABLE, BUT D=10 • 5 different types: HE, HO, IIA, IIB (closed only) I (open and closed) 1. 2. Strings high-energy processes Supergravity low-energy (& Geometry) ALL EQUIVALENT TO a MYSTERIOUS 11 D THEORY ! HOW IS THIS POSSIBLE ? ? A. Sagnotti – Astronomi. Amo, 23. 4. 2020 14

Dualities Solitons : energy “blobs” HEAVY particles • • Size: Compton: (Quantum Size) In String Theory : D- & other branes A. Sagnotti – Astronomi. Amo, 23. 4. 2020 15

10 D-11 D String Dualities How can different string theories be equivalent? Maps connect string modes and solitons (=“branes”) 1 2 A : . . . B : A. Sagnotti – Astronomi. Amo, 23. 4. 2020 16

Extra Dimensions • We perceive 4 dimensions (D=4, 3 + “time”). How could we be in D=10 o 11 without knowing it ? • Look at a long cylinder from farther and farther away 1 D 2 D “Small” extra dimensions would be “invisible” also to elementary particles (their “waves” would not fit) ? Which shape and why? A. Sagnotti – Astronomi. Amo, 23. 4. 2020 ? 17

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Ad. S/CFT & Thick Strings “OPEN” “LOOPS” or “CLOSED” “TREES” ? Effective “thick” string ! “QFT on Ad. S boundary String Theory in Ad. S bulk” A. Sagnotti – Astronomi. Amo, 23. 4. 2020 19

Black-Hole Entropy (? ) BH Thermodynamics: what, microscopically ? (SUSY) BH allow two computations: a) strong-coupling ( ~ GN 0) : Supergravity b) weak-coupling ( ~ GN=0) : String Theory Black Hole w Horizon BH entropy: horizon degrees of freedom BUT: what are we counting? A. Sagnotti – Astronomi. Amo, 23. 4. 2020 D-Branes 20

Outlook Remarkably rich (apparently UNIQUE) framework BUT : Why a given “shape” of the extra dimensions ? [CRUCIAL, CRUCIAL it determines the predictions for , …] What is String Theory ? A. Sagnotti – Astronomi. Amo, 23. 4. 2020 21

Some References • “The Incomplete Revolutions of String Theory”, Il Saggiatore 35 (2019) n. 4, p. 47, and refs. therein. • “Stringhe, Brane e Supergravità”, Ithaca: Viaggio nella Scienza XII, 2018, p. 161, and refs. therein. • “Teoria delle Stringhe”, in Enciclopedia della Scienza e della Tecnica, 2003, Ist. Enciclopedia Italiana, and refs. therein. Can be downloaded from: sns. it/it/sagnotti-augusto or from: sns. academia. edu/Augusto Sagnotti A. Sagnotti – Astronomi. Amo, 23. 4. 2020 22