Lecture Series on
"Conformal Field Theories, Trace Anomalies
and Their Applications"
July 3rd to 7th, 2017
Bethe Center for Theoretical Physics
Max Planck Institute for Gravitational Physics
I will introduce general properties of conformal
(quantum) field theories in arbitrary dimensions.
In even dimensions, the symmetry is anomalous,
giving rise to a conformal or Weyl anomaly. This
will be studied in both the unbroken and the
spontaneously broken phase. Using anomaly
matching leads to a proof of the a-theorem in
Conformal field theories often have moduli,
i.e. exactly marginal deformations. In their presence
new anomalies arise and they can be used, in the
favourable case of sufficient supersymmetry, to
constrain the sphere partition function in terms
of geometric data of the so-called conformal manifold.