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’!