Download Theoretical Particle

알기 쉬운 초끈 이론
2006.05.10
박 재모 (Postech)
Outline
Partcle physics
2. Black holes
3. String theory
4. M theory
5. D branes
6. Gauge/Gravity theory correspondence
7. Conclusions
1.
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( e    )
quarks: u
s
t
d
b
c
Bosons : mediating the forces between
fermions
photons (light) no self interactions
electromagnetic interactions
gluons : quarks, nuclear force

W, Z : weak interactions,  decay
gravitons : gravitational interactions
Relativistic Quantum Field Theory
Basic tools in theoretical particle physics
 Combination of special relativity and
the quantum
mechanics
2
p
-> E 2  p 2c 2  m2c 4
E 
2m
 particle and antiparticle
> 2mc 2 pair creation and annihilation occur
E
 infinite degrees of freedom
 strong, weak, electromagnetic interactions
well described-> standard model

The emergence of the force
Qq
r2
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 Et  h

Gauge theories
Gauge symmetry; electromagnetism
depend only on the electric field and
magnetic field strength. There are several
choices for the scalar potential

 
and the vector potential. A  A  
 Theories describing electromagentic,
strong and weak interactions have
this property -> gauge theory

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)
1
2
-> time
3
4
+
+
g
g
(virtual bosons created
and annihilated)
1  2   3  4
2
QED and QCD
QED (quantum electrodynamics)
interacting theory of photon and electron
2
e
g =
~ 10 2
(magnitude of charges)
hc
(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

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

GMm

 mc 2  0
r
GM
r  R
c2
R; black hole radius
For the mass of sun, R few km
(extremely dense object)
Black hole theormodynamics
Black hole has temperature and entropy
1
1. Black hole temperature
M
Black hole is not black
(Hawking radiation; black body
radiation with T  1
)

M
2. Black hole entropy is proportional
to the surface area S /(10 33 cm) 2
76
very large number 10
for a black
hole of solar mass
 Entropy ~ number of states (?)
 Classically black hole has few
parameters
(mass, charge and angular momentum)
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 pointlike 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
(
E  h  mc 2 )
String interactions

Joining splitting
interactions
1
3
2
->
Perturbation theory
g
g
g
2
g
3
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
1019 GeV
( string tension: Planck scale
proton 1GeV 0.17 mg )

Extra dimensions
Qq
r2
Coulomb’s Law
GMm
Newton’s Law
r2
 Kaluza-Klein theory
5 dimensional gravity unifies
electromagnetism and gravity
( graviton living on a very small circle
looks like a photon for 4d observer)

S1
-> 4d

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
1
is quantized in units of
R
 Periodic condition e ipR  1

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
(large g), one theory in 11 dimensions
(M theory)

Stringy geometry
The geometry as seen by a string is
quite different from that as seen by a
pointlike particle.
 Existence of the minimal length
(string scale)
1
or the symmetry R  

R
Winding modes of strings

Strings can wrap around a circle.
The momentum mode is proportional
to R

m
p 
 nR
R
1
 R 
R
symmetry corresponds to
the exchange of the winding modes and
the Kaluza-Klein modes ( 1 )
R
 This is called the T-duality.
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
small g
large radius
large g
M theory and 5 string theories
String vs. Membrane

Closed string

Open string
String theory is not just a theory
of strings
Extended objects
Strings and membranes
 D branes
Open strings can have Dirichlet
boundary conditions. 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 constants
D-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
number 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

AdS 5 X

S5
Exciting possibilities to understand
QCD using the string theory or the gravity
Large N gauge theory as a string
theory
Large N means we have many kinds
of gluons ( N 2)
 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.

What can we do with this
correspondence?
We can understand strong coupling
behavior 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
string 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 10 122
 Underlying principle of the string theory?

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!
