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This article 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  = 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 is the technique of so‐called space‐time dependent couplings (also known as “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  = 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.

Quantum field theories coupled to supergravity