In this thesis we study a particular realization of the Domain wall/Quantum Field Theory correspondence, a modification of the Anti de-Sitter/Conformal Field Theory correspondence that is used to study deformations of a Conformal Field Theory. In theQuantum gravity side of the duality we analyze a N = 1 gauged supergravity theory in 7 dimensions which presents two different Anti de-Sitter vacua, one of which preserves the full supersymmetry and one that breaks half of the supercharges. We will find a scalar 1/2-BPS solitonic solution describing a domain wall in an asymptotically Anti de-Sitter spacetime which interpolates between the supersymmetric AdS vacuum and a divergent AdS space situated at infinity, and we will calculate its tension and the effective mass of the scalar field when evaluated at the AdS vacuum. The dual theory of our gauged  supergravity is the 6-dimensional N = (1,0) Superconformal Field Theory, and the scalar 1/2-BPS field is dual to two relevant operators that induce a relevant deformation of the SCFT which can be identified with a renormalization group-flow. Here we will first compute the scaling dimension and the one-point functions of these operators in the SCFT, as well as indicating how to compute the two-point and three-point functions, and then we will study the c-function along the renormalization group-flow they induce and the beta function that characterizes this flow in order to derive some properties of the resulting Quantum Field Theory.