Gravity, Strings and Branesicc.ub.edu/~gomis/documents/2005/FQfinal.pdf · Gravity, Strings and...
Transcript of Gravity, Strings and Branesicc.ub.edu/~gomis/documents/2005/FQfinal.pdf · Gravity, Strings and...
Gravity, Strings and Branes Joaquim Gomis
International Francqui Chair
Inaugural Lecture Leuven, 11 February 2005
Fundamental Forces
Electroweak
• Strong
• Weak
• Electromagnetism
• Gravity
SM
QCD
Standard Model
• Basic building blocks, quarks, gluons, leptons
• Physics at different scales are separated in flat space time. Renormalization group
Standard Model
• Standard Model is a Relativistic Quantum Field Theory of Point Particles
• Is a Fundamental Theory? No
• It is an effective theory
L=F2µν+ Non-renormalizable terms
Gravity
• Gravity is universally atractive
• It is weak
Gravity
Electron Proton 1m
Felec » 10-28 Newtons
Fgrav »10-65 Newtons Gravity is negligible
• It is cumulative.
Objects fall on earth
General Relativity
• Newton’s theory does not obey special relativity (instantaneous interaction)
• Einstein space-time is curved • Gravity is due to space time curvature
General Relativity
• Gravity changes the flow of time. An observer far from a heavy mass sees the time going faster than an observer close to it
Special Relativity
• Time flows diferently for observes that move relative each other.
Cosmology • The Universe is homogeneous and isotropic at
large scales. • The Universe looks the same from any galaxy if
a galaxy at distance r has velocity
• Universe is expanding at “rate” H0
Cosmology • Age of Universe » 1018 sec
• Look out in space = Look back in time
• LUniv» c/H0» 1027m (now)
Cosmology
• Expansion cools the universe. We now see a CMB radiation. T» 3K
• Cosmolgical Horizon at T=1 (Big Bang)
Cosmic Microwave Radiation
WMAP (Wilkinson Microwave Anisotropy Probe)
CMB
Black Hole
• No object can collapse to a point. It first becomes a black hole
• Schwarzschild radius
Black Hole
• Sun, rh=3Km • Earth, rh=1cm • Gravity is very important to objects of any
size if they are sufficiently dense.
• Redshift factor=
Black Hole
• The horizon is the surface where the time slows to halt
• There is a singularity at r=0
Black Hole • Universality. The final shape of a black hole as seen from
outside is independent of how we make it. • The laws of quantum mechanics imply that black
holes emit thermal radiation. Hawking radition.
Black Hole
• Puzzles Information loss
Entropy of black holes
Quantum Gravity
• To understand cosmology we need a a theory of gravity at Planck length (10-33 cm). Quantum Gravity
Einstein-Hilbert lagrangian +Non-renormalizable terms are the effective theory of Quantum Gravity
Effective Field Theory
• Scattering of gravitons at low energy
String Theory
• What is Quantum Gravity?
• Which are the building blocks at Planck scale?
String Theory
• Open T=m2
s
• Closed
T → String Tension
ls» 10-33cm
String Theory
• Vibrations of string are the ordinary point particles
Photon
Graviton
String Theory
• Strings live in higher dimensions • Extra dimensions are curved.
R’
R
Moduli Moduli
R1
R2
R
V
Interaction of strings
Supersymmetry
• Symmetry among bosons and fermions
• Superstrings have no tachyon and live in 10 dimensions • Low energy descrpition is given by
supergravity
Dbranes
U(1) gauge theory
U(2) YM theory
D-branes
• D-branes at low energies are described by supersymmetric non abelian field
theories. • At weak coupling D-branes become fat
and are described by classical supergravity configuration.
Holography
• Hologram captures a 3d image in 2d
• Any piece of hologram captures the whole image , but in fuzzy form
Hologram
Holography and Black Holes
• Holography in quantum gravity: Number of degrees of freedom grows like
the area. • Entropy of a black hole » Area
Holography in String Theory
• Physics in the interior of some space-times can be described by ordinary
gauge theory of particles on the boundary
Holography in String Theory
• Space time emerges due to the interaction of particles living on the
boundary
M theory
• Non-perturbative formulation of string theory in 11d.
• Non-commutative geometry and M-branes
Tests of String Theory
• Planck Physics at accelerators? Effective Planck lenght of few Tevs • Violation of Lorentz symmetry.
Cosmic strings
• Cosmic strings produced at the early Universe
• The universe expands and strings will also expand. Cosmic strings could be as big as the visible universe
• Possible detection through gravitational waves or gravitational lensing
Cosmic Strings
Conclusions
• Strings and branes may provide an explanation of the Physics at small and large scales.
• String theory is a theory under construction.
Which is the guideline principle? • Can String Theory be tested
experimentaly?