Gravity, Strings and Branes

Transcription

1 Gravity, Strings and Branes Joaquim Gomis Universitat Barcelona Miami, 23 April 2009

2 Fundamental Forces Strong Weak Electromagnetism QCD Electroweak SM Gravity

3 Standard Model Basic building blocks, quarks, gluons, leptons Physics at different scales are separated in flat space time. Renormalization group

4 Standard Model Standard Model is a Relativistic Quantum Field Theory of Point Particles Is a Fundamental Theory? It is an effective theory No

5 Photons Effective Lagrangian

6 Gravity Gravity is universally atractive It is weak

7 Gravity Electron Proton 1m F elec» Newtons F grav»10-65 Newtons Gravity is negligible It is cumulative. Objects fall on earth

8 General Relativity Newton s theory does not obey special relativity (instantaneous interaction) Einstein space-time is curved Gravity is due to space time curvature

9 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

10 Special Relativity Time flows diferently for observers that move relative each other.

11 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 H 0

12 Cosmology Age of Universe» sec Look out in space = Look back in time L Univ» c/h 0» m (now)

13 Cosmology Expansion cools the universe. We now see a CMB radiation. T» 3K Cosmolgical Horizon at T=1 (Big Bang)

14 Cosmic Microwave Radiation WMAP (Wilkinson Microwave Anisotropy Probe) CMB

15 Black Hole No object can collapse to a point. It first becomes a black hole Schwarzschild radius

16 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=

17 Black Hole The horizon is the surface where the time slows to halt There is a singularity at r=0

18 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.

19 Black Hole Puzzles Information loss Entropy of black holes. Count Microscopic states.

20 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

21 Effective Field Theory Scattering of gravitons at low energy

22 Effective Lagrangian

23 String Theory What is Quantum Gravity? Which are the building blocks at Planck scale?

24 String Theory Open T String Tension T=m 2 s l s» cm Closed

25 String Theory Vibrations of string are the ordinary point particles Photon Graviton

26 Relativistic Particle action

27 String action

28 Mass spectrum closed bosonic string

29 String Theory Strings live in higher dimensions Extra dimensions are curved. Internal manifolds: Calabi-Yau spaces R R

30 3d view Calabi-Yau Space

31 Moduli Potential for moduli fields V R 2 R R 1

32 Interaction of strings

33 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

34 Supersymmetric String Theories

35 M theory Non-perturbative formulation of string theory in 11d. Non-commutative geometry and M-branes

36 Dualities

37 Dbranes U(1) gauge theory U(2) YM theory

38 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.

39 Low energy action of N Dbranes

40 Holography Hologram captures a 3d image in 2d Any piece of hologram captures the whole image, but in fuzzy form

41 Hologram

42 Holography and Black Holes Holography in quantum gravity: Number of degrees of freedom grows like the area. Entropy of a black hole» Area

43 Holography in String Theory Physics in the interior of some spacetimes can be described by ordinary gauge theory of particles on the boundary

44 N=4SYM/IIB string

45 Holography in String Theory Space time emerges due to the interaction of particles living on the boundary

46 Metric

47

48 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

49 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?

50 Schrodinger symmetry Galilei symmetry Dilatations Expansions

51 Bulk metric

52 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

53 Strongly coupled condensed matter systems?

54 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

55 Cosmic Strings

56 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?

57 Thanks