Holographic RG-flows and the Domain-Wall/Cosmology correspondence

In this master thesis we investigate implications of the Domain-Wall/Cosmology (DW/C) correspondence on one-point functions of holographic RG-flows. The thesis gives a detailed computation of linearized gauge-invariant Einstein equations in (d+1) dimensions while making the DW/C correspondence explicit. Although holographic renormalization has previously been studied on Lorentzian manifolds, we extend its study to Lorentzian domain-wall solutions with a parameter η. This parameter is introduced to easily travel from domain-walls to cosmologies in the context of the DW/C correspondence. We present the calculation of the vacuum expectation value of general scalar boundary operators of conformal weight Δ dual to a (d+1)-dimensional bulk theory, while still making the DW/C correspondence appear explicitly. Finally, we study the application of these results to holographic RG-flow solutions. In particular, the GPPZ solution is investigated in the framework of the thesis. We find that the vacuum expectation value of the scalar field is invariant under the domain-wall/cosmology correspondence