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?