Gravity, Strings and Branes Joaquim Gomis

Universitat Barcelona

Miami, 23 April 2009

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

Photons Effective Lagrangian

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 observers 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 v

•  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. No hair. Black holes are characterized by mass, electric

charge and and angular momenta The laws of quantum mechanics imply that black holes

emit thermal radiation. Hawking radition.

Black Hole

•  Puzzles Information loss

Entropy of black holes. Count Microscopic states.

Quantum Gravity

To understand (early time) cosmology we need 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

Effective Lagrangian

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

Relativistic Particle action

String action

Mass spectrum closed bosonic string

String Theory

•  Strings live in higher dimensions •  Extra dimensions are curved. •  Internal manifolds: Calabi-Yau spaces

R’

R

Calabi-Yau Space

3d view

Moduli

Potential for moduli fields

Moduli

R1

R2

R

V

Interaction of strings

Supersymmetry

•  Symmetry among bosons and fermions •  Number of bosons=Number of fermions

•  Superstrings have no tachyon and live in 10 dimensions •  Low energy descrpition is given by

supergravity

Supersymmetric String Theories

M theory

•  Non-perturbative formulation of string theory in 11d.

•  Non-commutative geometry and M-branes

Dualities

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.

Low energy action of N Dbranes

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

N=4SYM/IIB string

Holography in String Theory

•  Space time emerges due to the interaction of particles living on the

boundary

Metric

Physical Consequences

•  Strongly coupled gauge theories can be described by classical supergravity calculations

•  AdS correspondence at string level BMN sector Integrable structures Non-relatvistic strings

NRAdS/CMP correspondence

•  Can be apply holgraphic ideas to condensed matter systems?

•  Consider a non-relativistic theory on the boundary (screen). Which is the metric in the bulk?

Schrodinger symmetry

•  Galilei symmetry

•  Dilatations

•  Expansions

Bulk metric

Tests of String Theory

•  Planck Physics at accelerators? Effective Planck lenght of few Tevs. Large extra dimensions at LHC??? •  Violation of Lorentz symmetry. Many proposals Very Special relativity

•  Strongly coupled condensed matter systems?

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? Possible of Infinite algebras •  Can String Theory be tested

experimentaly?

Thanks