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In this thesis we give a pedagogical introduction to the construction ofNS5-D6(-O6)-D8(-O8) brane setups in massive type IIA string theory and thesix-dimensional $(1,0)$ SCFT's they engineer. After describing how to introducethe various ingredients (and their interplay) in type IIA, we explain how toread off an effective linear quiver description of the SCFT's from the branesetups. We then explain in detail how to construct all AdS$_7$ solutions ofmassive IIA supergravity which are dual to the field theories. We do this byexploiting the power of generalized complex geometry. We then show how toestablish a holographic dictionary between four-dimensional $\mathcal{N}=1$compactifications on a Riemann surface (without punctures) of the $(1,0)$SCFT's and a certain class of massive IIA AdS$_5$ solutions, which are inone-to-one correspondence with the AdS$_7$ vacua. We provide evidence for theadvocated AdS$_7$/CFT$_6$ and AdS$_5$/CFT$_4$ dualities by computing the(leading order of the) field theory $a$ conformal anomaly from supergravity.Finally, we briefly touch upon the construction of five-dimensional$\mathcal{N}=1$ SCFT's through fivebrane webs, and reduce the classificationproblem of their type IIB AdS$_6$ duals to a system of two coupled PDEs.

Higher-dimensional field theories from type II supergravity