Vortrag Ron Donagi am 25.5. um 18 Uhr

Titel:  From strings to standard models

Abstract:

The Standard Model encodes much of what we know about particle physics:
the three forces (electromagnetism, weak and strong nuclear forces)
associated with the gauge group U(1)xSU(2)xSU(3); the known particles:
quarks (which make up protons and neutrons) and leptons (electrons,
neutrinos), each recurring in three "generations"; and the precise rules
that determine which interactions of particles and forces can occur and
which are excluded. Our best hope of combining this tremendously
successful quantum theory of the three forces with the remaining force,
gravity (i.e. with general relativity), is based on String Theory and
M-Theory.

The goal of this talk is to discuss some recent attempts to explicitly
derive the Standard Model, via a "Grand Unified Theory", from Heterotic
String Theory.  Determination of the particle content of a given heterotic
compactification boils down to calculation of the cohomology of various
stable vector bundles over Calabi-Yau threefolds. We will discuss some of
the mathematical techniques involved in these calculations when the CY has
either an elliptic fibration (leading to Grand Unified theories) or a
genus one fibration (leading to Standard-Model-like theories). We will
also discuss some of the physics applications of our results. Key
mathematical tools include group theory (e.g. centralizers of finite
subgroups in compact Lie groups and their representation theory);
techniques for construction of Calabi-Yau manifolds (toric geometry,
elliptic fibrations, orbifolds); construction of interesting vector
bundles on a given manifold (monads, Fourier-Mukai transform); and
explicit calculation of various cohomology groups and related invariants.
I will describe how close to the Standard Model we have been able to get,
and how we expect to solve some of the remaining problems.