Mirjam Cvetič, University of Pennsylvania, Philadelphia, USA String theory and quests for unification of fundamental forces of nature http://obc2012.outofthebox.si/

1. String Theory and Geometry:
Quests to Unify Forces
of Nature
Mirjam Cvetič

2. Geometry and Physics have a long joint history,
dating all the way back to the Greek philosophers.

3. Modern examples of such
deep links:
Einstein’s theory of Gravity
&
Unification of forces with
quantum gravity within
string theory
Review these deep links
between geometry and
physics in the context of
string theory.

4. Birth of Modern Physics: Newton’s Mechanics
Newton

5. Apple: Where it all started!

6. Gravitational Force on Earth  Classical Mechanics

7. Solar System

8. Milky Way

9. Gravitational forces in
FLAT SPACE (3-space dimensions)

10. Add time (fourth dimension)  space & time not flat!
Einstein Theory of Gravity

11. Geometry of space-time is curved due to matter
matter curvature

12. Particles move on geodesics

13. curvature + geodesic  looks like force

14. The planetary orbits can now be explained geometrically:
Sun curves spacetime and planets follow geodesics

15. Theory is relevant also for cosmological questions
of the Early Universe

16. Another Feature of Nature:
Particles are ``fuzzy’’ at smaller scales
Cannot pinpoint both, its location x &its momentum p

17. Bohr

18. Quantum mechanics was born

19. Principle of quantum mechanics valid also
at nuclear and sub-nuclear scales (<10-18 cm)

20. These ideas were checked by scattering
experiments of high energy particles such as
LARGE HADRON COLLIDER IN GENEVA

21. Feynman

22. Interaction takes place by exchange of
virtual particles- Feynman diagrams

23. Quantum Field Theory of point particles 
STANDARD MODEL

24. Gravity+Quantum Mechanics ?

25. Particles+quantum mechanics+gravity  infinities
Difficult to make sense of !

26. Green&Schwarz’84
Strings come to the rescue!
 remove infinities

27. quark
At yet smaller scales ``elementary particles’’
look like excitation of strings

28. graviton
Graviton (particle that mediates gravitational interactions)
always appears as another excitation of strings
 string theory contains quantum gravity!

30. Joining & splitting of strings
Interactions ``softer’’
No infinities!

31. String interactions are described by the beautiful
geometry of two-dimensional (Riemann) surfaces

32. Everything seems to be in place: consistent
quantum theory of all particles which appear as
string excitations at very tiny (10-33 cm) scales

33. Smooth geometry of strings seems to
explain all known quantum interactions,
including quantum gravity!

34. String’s connection between geometry and
physics ``more complex’’:
String theory (as consistent quantum theory)
demands that space-time not be
four dimensional, but ten dimensional!
How can we hope to use string theory to
answer questions relevant to four-dimensional
physics?!

35. We demand that the extra dimensions be curled
up into a tiny compact space, thus rendering it
unobservable and avoiding a direct clash with
experiments.
Not totally satisfactory: What are the extra
dimensions good for?!

36. But this answer is not totally
satisfactory:
What are the extra dimensions
good for?!

37. New Insights: D(irichlet)-branes
(boundaries of open strings) Polchinski’96

38. String Theory with D-branes - Brane World
U(2)
U(3)
U(1)
Matter on & at intersection of D-branes in additional
dimensions-GEOMETRIC! [Cvetič-Shiu-Uranga Model (2001)
-first three-family supersymmetric Standard Model]

39. Modern String Theory Insights into Black Holes:
Bekenstein-Hawking black hole entropy:
S=¼ Ahorizon
Ahorizon= area of the black hole horizon
Where do black hole microscopic degrees come from?

40. Black hole as wrapped
D-branes in the
Internal dimensions
Microscopic degrees are string
excitations on D-branes=
Black Hole Entropy!
Strominger-Vafa ‘96
Prototype of such black holes:
Cvetič-Youm dyons (1995)

41. We have gained important insights
into our quest of unifying forces of
of nature, including quantum gravity!
Uncovering deep links between
Geometry and Physics!
A lot remains to be understood &
remains a `work in progress’!