Quantum field theories coupled to supergravity

This dissertation is devoted to the investigation of the interplay
of supersymmetric Yang-Mills theories (SYM) and supergravity
(SUGRA). The topic is studied from two points of view: Firstly from
the point of view of AdS/CFT correspondence, which realises the
coupling of four dimensional superconformal N=4 SYM theory and ten
dimensional type IIB SUGRA in a holographic way. In order to arrive
at theories that resemble quantum chromodynamics (QCD) more
closely, fundamental fields are introduced using probe D7-branes
and non-trivial background configuration are considered. In
particular supergravity solutions that are only asymptotically
anti-de Sitter and break supersymmetry are used. This allows the
description of spontaneous chiral symmetry breaking. The meson
spectrum is calculated and the existence of an associated Goldstone
mode is demonstrated. Moreover it is shown that highly radially
excited mesons are not degenerate. Additionally instanton
configurations on the D7-branes are investigated, which lead to a
holographic description of the dual field theory's Higgs branch.
Finally a holographic description of heavy-light mesons is
developed, which are mesons consisting of quarks with a large mass
difference, such that a treatment of B mesons can be achieved. The
second approach to the topic of this thesis is the technique of
so-called space-time dependent couplings ("local couplings"), where
coupling constants are promoted to external sources. This allows to
explore the conformal anomaly of quantum field theories coupled to
a classical gravity background. The technique is extended to the
superfield description of N=1 supergravity, a complete basis for
the anomaly is given and the consistency conditions that arise from
a cohomological treatment are calculated. Possible implications for
an extension of Zamolodchikov's c-theorem to four dimensional
supersymmetric quantum field theories are discussed.