알기 쉬운 초끈 이론

2006.05.10박 재모 (Postech)

Outline1. Partcle physics2. Black holes3. String theory4. M theory5. D branes6. Gauge/Gravity theory correspondence7. Conclusions

particle physics Study of fundamental interactions of fundamental particles in Nature Fundamental interactions 1. strong interactions 2. weak interactions 3. electromagnetic interactions 4. gravitational interactions

Fundamental Particles Fermions : building blocks of matter Paulis’s exclusion principle leptons: electron(e), muon( ), tau( ) neutrinos( ) quarks: u s t d b c

e

Bosons : mediating the forces between fermions photons (light) no self interactions electromagnetic interactions gluons : quarks, nuclear force W, : weak interactions, decay gravitons : gravitational interactions

Z

Relativistic Quantum Field Theory

Basic tools in theoretical particle physics Combination of special relativity and the quantum mechanics -> particle and antiparticle > pair creation and annihilation

occur infinite degrees of freedom strong, weak, electromagnetic interactions well described-> standard model

mpE2

2

42222 cmcpE

E 22mc

The emergence of the force Coulomb force When electrons emit and absorb (virtual) photons, momentum transfer occurs. Coulomb force is generated by this process. Virtual photons are those not satisfying energy-time uncertainty relation

2rQq

htE

Gauge theories Gauge symmetry; electromagnetism depend only on the electric field and magnetic field strength. There are several ch

oices for the scalar potential and the vector potential. Theories describing electromagentic, strong and weak interactions have this property -> gauge theory

AA

Abelian and non-abelian gauge theories

Photons, mediator of the electromagnetic force do not have self interactions,

carry no charge -> abelian (dielectric effects, charge screening)

e

Gluons, mediator of the strong interactions do have self interactions, carry charges

-> Non-abelian (charge antiscreening, asympotic degrees of freedom) Weak interactions are also non-Abelian)

Interactions of a field theory(perturbation theory)

+ +

-> time (virtual bosons created and annihilated)

g

1

2

3

4

4321

2g

QED and QCD QED (quantum electrodynamics) interacting theory of photon and electron g = ~ (magnitude of charges) (series expansion works well) QCD (quantum chronodynamics) interacting theory of quarks and gluons g~1 (series expansion does not work) colors; charges carried by quarks and gluons

210

che2

Classical Gravity General Relativity matter and energy make spacetime curved

Black Holes Gravitational field is so strong, once the light is trapped it cannot escape. Heuristically

R; black hole radiusFor the mass of sun, R few km (extremely dense object)

02 mcr

GMm

2cGMRr

Black hole theormodynamics

Black hole has temperature and entropy

1. Black hole temperature Black hole is not black (Hawking radiation; black body radiation with )

M1

MT 1

2. Black hole entropy is proportional to the surface area very large number for a black hole of solar mass Entropy ~ number of states (?) Classically black hole has few

parameters (mass, charge and angular momentum)

233 )10/( cmS

7610

Entropy of 3K radiation of the size of 1 million light year

Precursor of field theory/gravity correspondence Black hole entropy is proportional to the surface area in contrast of the of the usual behavior ~ volume (field theory behavior) Degrees of freedom of the gravity theory in D dimensions match with those of field theory in D-1 dimensions.

Quantum Gravity Possible only by string theory (modify the bad short distance behavior of the p

ointlike particle)

pointlike particles at the point of interactions due to the uncertainty principle infinite momenta can contribute while such singular behavior is smoothed out by the stringy behavior

String theory Open string -> photon, gluons Closed string -> graviton

Particles from Strings particle: string symphony eigenmodes of the string oscillation ( )

2mchE

String interactions Joining splitting

interactions

->

1

2

3

Perturbation theory

g

g 2g 3g

Supersymmetry Symmetry between bosons and fermions The vacuum fluctuations between the bosons and the fermions cancel Essential in obtaining the massless particles such as photons and gravitons ( string tension: Planck scale proton 0.17 mg )

GeV1910

GeV1

Extra dimensions Coulomb’s Law Newton’s Law Kaluza-Klein theory 5 dimensional gravity unifies electromagnetism and gravity ( graviton living on a very small circle looks like a photon for 4d observer) -> 4d

2rQq

2rGMm

1S

If we go to higher dimensions than 5 we can incorporate the other forces in Nature. <- weak interactions strong interactions

How do we know extra dimensions? By spectroscopy The situation is similar to solving quantum mechanics of 1 dimensional box with length R The momentum of the particle is quantized in units of Periodic condition

R1

1ipRe

String revolution 1st string revolution (1984) consistency of the string theory 5 string theories in 10 dimensions defined perturbatively (small g) 2nd string revolution nonperturbative behavior of string theory (lar

ge g), one theory in 11 dimensions (M theory)

Stringy geometry The geometry as seen by a string is quite di

fferent from that as seen by a pointlike particle.

Existence of the minimal length (string scale) or the symmetry

RR 1

Winding modes of strings Strings can wrap around a circle. The momentum mode is proportional to R

symmetry corresponds to the exchange of the winding modes and the Kaluza-Klein modes ( )

This is called the T-duality.

RR 1

R1

nRRmp

From 10 dimensions to 4 dimensions In order to have 4 dimensional world we should make extra 6 dimensions very small. For technical reasons one looks for the solutions of the equation of the string theory with N=1 supersymmetry. The extra 6 dimensions

satisfy Calabi-Yau conditions. -> Calabi-Yau manifold.

Calabi-Yau manifold has similar symmetry to the T-duality called mirror symmetry. Basically this interchanges the higher dimensional analogue of genera of 2 dimensional surface.

Creation of the new dimension If one increases g, another

dimension is open!

-> small radius large radius small g large g

M theory and 5 string theories

String vs. Membrane Closed string

Open string

String theory is not just a theoryof strings Extended objects Strings and membranes D branes Open strings can have Dirichlet boundary c

onditions. The endpoints of the open strings are fixed to move in some fixed plane -> D branes

Dp-brane: p+1 dimensional object

Excitation of D brane -> open string contains photon or Maxwell field (It carries charge.)

D branes can interact with the closed strings ( gravity) ; dynamical objects (have masses)

It can have various shapes

D branes and black holes

If we vary the string coupling constantsD-branes become black holes or black branes (extended in higher dimensions

but looks like black holes in 4 dimensions)

By counting the number of states for D-branes, one can count the number of quantum states of black holes. (Strominger and Vafa 1996) This holds for the so called supersymmetric black holes where the numb

er of states do not change as the coupling varies.

Holographic principle Gravitational theory in D dimensions is equivalent to a field theory in D-1 dimensions.

AdS/CFT correspondence

D3 brane described by N=4 super Yang-Mills (non-Abelian) gauge theory (conformal) The geometry near the D3 branes

Exciting possibilities to understand QCD using the string theory or the gravity

XAdS 5 5S

Large N gauge theory as a string theory Large N means we have many kinds of gluons ( ) t’ Hooft shows that large N gauge theories can have perturbation expansions

similar to the string theory AdS/CFT or gauge/gravity correspondence is the avatar of this idea.

2N

What can we do with this correspondence? We can understand strong coupling behavio

r of QCD by looking at the geometry of the gravity side. Area law behavior of Wilson loops, relation between confinement and monopole condensation, existence of mass gap for glue ball states, glueball spectrum, chiral symmetry breaking

Conclusions String theory is a theory of quantum gravity

incorporating the other fundamental interactions in Nature.

We have microscopic understanding of the black hole thermodaynamics from string theory. We can understand (large N) QCD from stri

ng theory.

Future problems in string theory

Too many solutions exist from 10 dimensions to 4 dimensions Selection principle? or anthropic principle (Landscape) Cosmological constant in Planck units Underlying principle of the string theory?

12210

String theory after LHC (Large Hadron Collider) Will probe the region beyond the standard

model around 2008 One of the most exciting period Supersymmetry to be discovered String theory should explain the discoveries

at LHC; Great challenges ahead of us!