Gravity, Strings and Branes Joaquim Gomis International Francqui Chair Inaugural Lecture Leuven, 11 February 2005
Fundamental Forces Strong Weak Electromagnetism QCD Electroweak SM Gravity
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? It is an effective theory No L=F 2 µν + Non-renormalizable terms
Gravity Gravity is universally atractive It is weak
Gravity Electron Proton 1m F elec» 10-28 Newtons F grav»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 H 0
Cosmology Age of Universe» 10 18 sec Look out in space = Look back in time L Univ» c/h 0» 10 27 m (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, r h =3Km Earth, r h =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 String Tension T=m 2 s l s» 10-33 cm Closed
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 V R 2 R R 1
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 spacetimes 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?