A GRAND TOUR OF

HYPERMODERN PHYSICS- UNIFICATION GUTS STRINGS & BRANES

LECTURE 6

APR. 26, 2019 DR. GEORGE DERISE 1:30 – 3:30 PROFESSOR EMERITUS, MATHEMATICS TNCC THOMAS NELSON COMMUNITY COLLEGE ROOM 328. SPRING 2019

CLASSICAL- NEWTONIAN MECHANICS

TERRESTRIAL MECHANICS

CELESTIAL MECHANICS ELECTROMAGNETIC THEORY-MAXWELL

SPECIAL RELATIVITY - EINSTEIN

CLASSICAL NEWTONIAN c MECHANICS RELATIVISTIC MECHANICS

푬 = 풎풄ퟐ

CLASSICAL ELECTROMAGNETIC THEORY LORENTZ FOUR DIMENSIONAL SPACETIME TRANSFORMATIONS

ħ CLASSICAL QUANTUM NEWTONIAN MECHANICS MECHANICS – PHYSICS –

UNIFICATION

There is a fifth dimension beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between and shadow, between science and superstition, and it lies between the pit of man's fears and the summit of his knowledge. This is the dimension of imagination. It is an area which we call the twilight zone. Rod Serling

Hey Rod, the fifth dimension is just the kaluza klein theory unifying the interactions of and that of THE STANDARD MODEL SU(3) x SU(2) x U(1)

ENCOMPASSES THE STRONG WEAK AND ELECTROMAGNETIC INTERACTIONS

COMPLETELY DESCRIBES ALL THE PHYSICS CONDUCTED IN ACCELERATORS TO THE PRESENT TIME

NO DISCREPANCIES

10-3 PRECISION (SOME TO 10 DIGIT ACCURACY)

SU(3)

STANDARD MODEL; WHAT’S WRONG?

THREE INDEPENDENT COUPLING CONSTANTS, WHY THEIR VALUES?

FAMILY PROBLEM; WHY 3 FAMILIES OF AND ?

HIGGS MECHANISM

WHY THE MASSES OF THE ?

WHY CP SYMMETRY BREAKING IN -NOT IN STRONG

TOO MANY ARBITRARY PARAMETERS

WHY DOES THIS MODEL WORK?

WHY IS THERE MORE THAN ANTIMATTER?

WHAT ABOUT ? DARK ENERGY?

HIERARCHY PROBLEM; WHY m(H)<< m(PLANCK)

DOES NOT INCLUDE GRAVITY!

TWO PILLARS OF THEORETICAL PHYSICS GENERAL QUANTUM RELATIVITY MECHANICS

STANDARD MODEL STANDARD MODEL OF COSMOLOGY OF

Electromagnetism Gravity Strong nuclear force Weak nuclear force

Big Bang, Black Holes QUANTUM MECHANICS

Small; , subatomic particles Large; (apples?), planets, stars, galaxies

Linear equations Non linear equations Probabilistic Deterministic

Quantum fuzziness Exact trajectory THE AND SPLIT ALL ELEMENTARY PARTICLES ARE EITHER 0, 1, 2, . . . FORCES or SPIN 1/2, 3/2, . . . MATTER

SUPERSYMMETRY A HYPOTHETICAL SYMMETRY BETWEEN FERMIONS AND BOSONS.

For every known spin-1/2 particle type, there must be a spin 0 “” with the same charge and color and interactions.

For every known spin-1 particle (), there should be a spin 1/2 superpartner ( fermion).

The spin-0 has a spin-1/2 superpartner called the .

The spin-2 (the carrier of the gravitational force) has a superpartner with spin-3/2 called the .

21 Infinities generally arise because of the vertices. Fermions and Bosons contribute with opposite signs to the mass. Maybe they can be arranged to cancel?

Supersymmetry automatically provides exactly the cancellation needed to solve the hierarchy problem.

Supersymmetry must be a broken symmetry.

DESPERATELY SEEKING SUSY SUPERSYMMETRY ALL ELEMENTARY PARTICLES ARE EITHER BOSONS SPIN 0, 1, 2, . . . FORCES FERMIONS SPIN 1/2, 3/2, . . . MATTER

SUPER YANG MILLS THEORY: SUPERSYMMETRIC EXTENSIONS OF THE STANDARD MODEL explains inflation, large scale structure, the origin of Higgs mass, and the origin of right-handed mass and how the microwave background radiation appears isotropic..

SUPERGRAVITY (11 SPACETIME DIMENSIONS) THE SUPERSYMMETRIC GENERALIZATION OF EINSTEIN’S EQUATIONS OF GENERAL RELATIVITY

Supersymmetry solves the hierarchy problem.

SUSY provides an excellent candidate for dark matter: the spin ½ partner to the (lightest SUSY particle- the photino) is cosmologically stable. ALGEBRA OF SUPERSYMMETRY RUTHLESSLY SIMPLIFIED

RECALL: BOSONS SPIN 0, 1, 2, . . . FORCES FERMIONS SPIN 1/2, 3/2, . . . MATTER

EVEN ELEMENTS: Bα BOSE ELEMENTS ODD ELEMENTS: Fa FERMI ELEBENTS

[Bα, Bβ]≈ Bγ [Bα, Fa] ≈ Fb {Fa, Fb} ≈ Bα

SPACETIME GROUPS

3+3+1+3=10

EACH A SUBGROUP OF THE 10 DIMENSIONAL THE POINCARÉ GROUP

ALGEBRA OF MINKOWSKI SPACETIME- SPECIAL RELATIVITY

SUPERGRAVITY (11 SPACETIME DIMENSIONS) THE SUPERSYMMETRIC GENERALIZATION OF EINSTEIN’S EQUATIONS OF GENERAL RELATIVITY

STRINGS

ELEMENTARY 1 DIMENSIONAL MOVE THROUGH SPACETIME

VIBRATE Each vibrational mode of a string corresponds to a particle.

CAN JOIN, SPLIT, TWIST

OPEN OR CLOSED

HAVE A STRING TENSION α’ 풐(휶′) ∼ ퟏퟎퟑퟗ tons

The harmonics, or normal modes of vibration are determined by the tension of the string. a. Point particle- world line

b. String- world sheet

c. Closed string- world tube

VIOLENT FLUCTUATIONS OF SPACETIME AT THE PLANCK LENGTH ퟏퟎ−ퟑퟓ m

THE PROBLEM OF : FLUCTUATIONS OF THE METRIC ACTION: GENERALIZATION TO A STRING

LEAST ACTION PRINCIPLE: THE STRING SWEEPS OUT A WORLD SHEET OF MINIMAL SURFACE AREA STRINGS ‘LIVE’ IN SPACETIME OF 10 DIMENSIONS M10 = P4 X K6

NO ULTRA VIOLET (SHORT DISTANCE) DIVERGENCES

SUPERSYMMETRY IS NECESSARY FOR CONSISTENCY (HENCE: SUPERSTRINGS)

GRAVITONS EXIST; GENERAL RELATIVITY ‘POPS OUT OF THE AIR”

NON ABELIAN GAUGE THEORIES (YANG-MILLS THEORIES)

LOW ENERGY LIMIT, SUGRA + STANDARD MODEL

SUPERSTRING THEORY UNITES QUANTUM MECHANICS AND GENERAL RELATIVITY

A QUANTUM THEORY OF GRAVITY!! THICKENED FEYNMAN DIAGRAMS The interaction of two point particles portrayed by thickened Feynman diagrams.

Lines and points become tubes and surfaces.

Smearing of the interaction avoids the singularity at vertices

String Theory is not plagued by the infinities as in point particle quantum field theories.

Perturbation theory is used to expand the interaction into a sum of individual diagrams. First one: a tree-level diagram.

The others with increasing number of holes: loop diagrams.

If the interaction strength is small, (like QED)the series would converge rapidly, grows. PERTURBATIVE STRING THEORY g2 g4 g6 ORIGINAL BOSONIC THEORY, 26 DIMS

E8 X E8 HETEROTC STRING THEORY,HE

http://www.superstringtheory.com/ PRINCETON STRING QUARTET

Gross Harvey Martinec Rohm

THE HETEROTIC STRING

10 DIMENSIONAL 26 DIMENSIONAL

EXTRA 16 DIMENSIONS- (INTERNAL DIMENSIONS) RESPONSIBLE FOR SYMMETRIES OF THE YANG MILLS FORCES

SYMMETRY IN MATH

DUALITY DUAL POLYHEDRA

The centers of the faces of a cube are the vertices of a regular octahedron and

the centers of the faces of a regular octahedron are the vertices of a cube. Also works for the dodecahedron and the icosahedron DUALITY TRANSFORMATIONS WEB OF INTERCONNECTED STRING THEORIES

All five perturbative string theories are connected by DUALITIES. Also connected to an eleven dimensional theory that at low energies is described by supergravity.

Strings are not fundamental to M-theory P BRANES – D BRANES BRANE - a physical object generalizing the notion of a string to higher dimensions. They are dynamical objects which can propagate through spacetime They have mass and can have other attributes such as charge.

A p-dimensional brane is generally called "P-BRANE".

BLACK HOLES

CLASSICALLY: Black holes are black. They do not radiate. “BLACK HOLES HAVE NO HAIR” Mass, charge, angular momentum completely describes a black hole.

QUANTUM MECHANICALLY: Black holes are thermal radiators with a (Hawking) temperature and an entropy

BIG QUESTION: IS THERE A STATISTICAL MECHANICAL INTERPRETATION? This exact entropy formula can be derived microscopically by counting of quantum states of strings and D-branes which correspond to black holes in string theory. The class of black holes used (extremal black holes) are described by 5-branes, 1-branes and open strings traveling down the 1-brane all wrapped on a 5-dimensional torus, which gives an effective one dimensional object-a black hole.

A S= ퟒ BLACK HOLE ENTROPY FORMULA

Microscopic Origin of theBekenstein-Hawking Entropy Strominger- Vafa, 1996 THE HOLOGRAPHIC PRINCIPLE (t’Hooft 1993)

ALL OF THE INFORMATION CONTAINED IN SOME REGION OF SPACE CAN BE REPRESENTED AS A `HOLOGRAM' –

A THEORY WHICH `LIVES' ON THE BOUNDARY OF THAT REGION.

THE HOLOGRAPHIC PRINCIPLE was motivated by BLACK HOLE THERMODYNAMICS which conjectures that

THE MAXIMAL ENTROPY SCALES WITH THE AREA OF THE EVENT HORIZON, AND NOT THE VOLUME OF SPACE OF THE BLACK HOLE THE INFORMATIONAL CONTENT OF ALL THE OBJECTS THAT HAVE FALLEN INTO THE HOLE MIGHT BE ENTIRELY CONTAINED IN SURFACE FLUCTUATIONS OF THE EVENT HORIZON.

The entropy (or disorder) of a black hole is proportional to the surface area of the black hole, not its volume. This is one of the arguments in support of the holographic principle, BLACK HOLE INFORMATION PARADOX S: ENTROPY a measure of randomness; S counts the number of microscopic Quantum States.

BEKENSTEIN 1970: Black Holes have Entropy. S (black hole) ̴ A (event horizon)

PROBLEM: Entropy is a concept of Quantum Mechanics. Black Holes are a concept of General Relativity

FOUR LAWS OF BLACK HOLE MECHANICS – HAWKING et al. 1973

PARTICLE CREATION BY BLACK HOLES – HAWKING 1975. Black Holes have temperature and they emit particles. Black Holes evaporate. Throw ‘information’ (a mass) into a Black Hole. Black Holes evaporate. The information is that of the wave function ѱ, i.e. all the quantum numbers (information), e.g. mass, spin, charge are lost.

Schrodinger’s equation is one of time evolution; it predicts (probabilistically) the future. But the information disappears into the singularity.

HAWKING’S SOLUTION: The information comes out via the emitted particles. ADS-CFT

MALDACENA’S AdS5-CFT4 CORRESPONDENCE (1997)

FIRST ACTUAL EXAMPLE OF A QUANTUM FIELD THEORY THAT IS A THEORY OF GENERAL RELATIVITY.

A GRAVITATIONAL THEORY IS EQUIVALENT TO A QUANTUM THEORY!

TYPE IIB STRING THEORY ON THE SPACE ADS5 IS EQUIVALENT TO N = 4 SUPERSYMMETRIC YANG–MILLS THEORY ON THE FOUR-DIMENSIONAL BOUNDARY. MALDACENA’S AdS5-CFT4 CONJECTURE AdS: ANTI DE-SITTER SPACE maximally symmetric spacetime with negative curvature.

AdS5 : 5 DIMENSIONAL ANTI-DE-SITTER SPACE

CFT4: 4DIMENSIONAL CONFORMAL FIELD THEORY

An ordinary (non gravitational) field theory which is conformally invariant.

N = 4 SUPERSYMMETRIC YANG–MILLS THEORY SUPERSYMMETRIC: bosons and fermions are in the theory. YANG-MILLS THEORY: a theory of particle physics that uses non-Abelian groups. S(2) Electro-Weak and SU(3) Strong force theories are Yang-Mills.

N = 4: number of . CALABI YAU MANIFOLD (THE TINY 6 DIMENSIONAL SPACE)

M10 = P4 X K6

AN IMPORTANT IDENTITY: 10 = 4+6 √ 10 = 5+5 ?

A CALABI-YAU MANIFOLD WITH THE FIRST AND SIMPLEST HOMOTOPY GROUP (TOPOLOGY) (THE FUNDAMENTAL GROUP) IMPLIES ELECTRIC CHARGES OF A PARTICLE CAN TAKE ON EXOTIC FRACTIONAL VALUES e.g. 1 1 1 1 , , , 5 11 13 53 “PROFESSOR, WHAT IS E(8) ?”

A calculation the size of Manhattan!! It involves 453,060x 453,060 matrices each of whose entries is a polynomial of degree up to 22!! E8 X E8

E6 X E8

E6

SU(3) X SU(2) X U(1)

SU(2) X U(1)

SU(3) U(1) HOW MANY DIFFERENT CALABI YAUS? CONSERVATIVE ESTIMATE:

UNIFICATION OF FUNDAMENTAL THEORIES

Electricity 1864 Electromagnetism 1971 Light

Beta-decay 1976 Weak Interaction 1965 Standard Model 1973 STRING , etc. THEORY 1687 Earth Gravity 1916 ? Universal Gravity Celestial Mech. General Relativity Spacetime Geom. Spring 2008 54 WHAT IS THE LANDSCAPE? VAST ARRAY OF VACUUM STATES “DAS IST NICHT EINMAL FALSCH” “THIS IS NOT EVEN WRONG!!”

A NEW PHILOSOPHY OF SCIENCE?

THE UNREASONABLE EFFECTIVENESS OF MATHEMATICS IN THE NATURAL SCIENCES Eugene Wigner http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

LIE GROUPS: U(1) The Electromagnetic Interaction SU(2) The Weak Interaction SU(3) The Strong Interaction SU(3)XSU(2)XU(1) Standard Model of Particle Physics SU(5) A Grand Unified Theory (quarks and leptons) Poincare Group Special Relativity GRADE 2 LIE GROUPS SUPERSYMMETRY E(8)X(E8) The Gauge Group of the (?) (String Theory)