KTH/SU
Mathematics
Colloquium
February
21, 2007
Måns
Henningson,
Chalmers
Four-dimensional
quantum field theory: some surprises of the
simplest example
ABSTRACT:
Quantum
field theory has been immensely successful when
applied to physics:
Predictions from quantum electrodynamics agree with experiments to
a precision of up to ten significant digits. The standard model of elementary
particle physics has correctly predicted and described a wide variety
of phenomena. Further exciting developments are expected when the Large
Hadron Collider at CERN starts operating next year.
Mathematically the situation is more troublesome:
Despite many efforts, no non-trivial example of a quantum field theory in four
space-time dimensions has yet been rigorously constructed. To make progress
on this issue, it appears fruitful to consider
relatives of the theories that appear
in nature, but with larger amounts of (super)symmetry. Yang-Mills theories with
maximally extended supersymmetry are then a natural place to start.
In this talk, we will review some aspects of these beautiful and fascinating
theories. In particular, we will describe the by
now well established, but still
rather mysterious, S-duality property, which indicates that maybe these quantum
theories are neither four-dimensional nor field
theories after all...