Mirjam Cvetič
String Theory and Geometry: Quests to Unify Forces of Nature
Geometry and Physics have a long joint history, dating all the way back to the Greek philosophers.
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.
Newton
Birth of Modern Physics: Newton’s Mechanics
Apple: Where it all started!
Gravitational Force on Earth Classical Mechanics
Solar System
Milky Way
Gravitational forces in FLAT SPACE (3-space dimensions)
Add time (fourth dimension) space & time not flat! Einstein Theory of Gravity
Geometry of space-time is curved due to matter matter curvature
Particles move on geodesics
curvature + geodesic looks like force
The planetary orbits can now be explained geometrically: Sun curves spacetime and planets follow geodesics
Theory is relevant also for cosmological questions of the Early Universe
Another Feature of Nature: Particles are ``fuzzy’’ at smaller scales
Cannot pinpoint both, its location x &its momentum p
Bohr
Quantum mechanics was born
Principle of quantum mechanics valid also at nuclear and sub-nuclear scales (<10-18 cm)
These ideas were checked by scattering experiments of high energy particles such as LARGE HADRON COLLIDER IN GENEVA
Feynman
Interaction takes place by exchange of virtual particles- Feynman diagrams
Quantum Field Theory of point particles STANDARD MODEL
Gravity+Quantum Mechanics ?
Particles+quantum mechanics+gravity infinities
Difficult to make sense of !
Strings come to the rescue! remove infinities
Green&Schwarz’84
At yet smaller scales ``elementary particles’’ look like excitation of strings
quark
Graviton (particle that mediates gravitational interactions) always appears as another excitation of strings
graviton
string theory contains quantum gravity!
Joining & splitting of strings Interactions ``softer’’
No infinities!
String interactions are described by the beautiful geometry of two-dimensional (Riemann) surfaces
Everything seems to be in place: consistent quantum theory of all particles which appear as string excitations at very tiny (10-33 cm) scales
Smooth geometry of strings seems to explain all known quantum interactions, including quantum gravity!
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?!
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?!
But this answer is not totally satisfactory:
What are the extra dimensions good for?!
New Insights: D(irichlet)-branes (boundaries of open strings) Polchinski’96
Matter on & at intersection of D-branes in additional dimensions-GEOMETRIC! [Cvetič-Shiu-Uranga Model (2001) -first three-family supersymmetric Standard Model]
U(3) U(1)
U(2)
String Theory with D-branes - Brane World
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?
Black hole as wrapped D-branes in the Internal dimensions
Prototype of such black holes: Cvetič-Youm dyons (1995)
Microscopic degrees are string excitations on D-branes= Black Hole Entropy! Strominger-Vafa ‘96
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’!