Integrability and chaos in super Yang-Mills theories from anomalous-dimension spectra

The discovery of integrability in planar maximally supersymmetric
Yang-Mills (SYM) theory led to considerable advances in the exact
computation of its CFT data. In this talk I will review these advances
and discuss universal statistical properties of anomalous-dimension
spectra in SYM theories in the planar limit and at finite rank of the
gauge group. I will show how they can give insight into the nature of
the underlying model, in particular we will see integrability manifest
itself in the planar integrable limit of certain SYM theories, while
non-integrable spectra can be described by random matrix theory,
indicating their quantum-chaotic nature.