We review the formalism of holographic renormalization. We start by discussing
mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the …

We systematically develop the procedure of holographic renormalization for RG flows dual
to asymptotically AdS domain walls. All divergences of the on-shell bulk action can be …

In these lecture notes we first assemble the basic ingredients of supersymmetric gauge
theories (particularly N= 4 super-Yang-Mills theory), supergravity, and superstring theory …

We discuss the computation of correlation functions in holographic RG flows. The method
utilizes a recently developed hamiltonian version of holographic renormalization and it is …

An improved correspondence formula is proposed for the calculation of correlation functions
of a conformal field theory perturbed by multi-trace operators from the analysis of the …

We will demonstrate that the generalized uncertainty principle exists because of the
derivative expansion in the effective field theories. This is because in the framework of the …

We consider gauge/string duality (in the supergravity approximation) for confining gauge
theories. The system under scrutiny is a 5-dimensional consistent truncation of type IIB …

We perform a holographic renormalization of cascading gauge theories. Specifically, we find
the counterterms that need to be added to the gravitational action of the backgrounds dual to …

Building on earlier results on holographic bulk dynamics in confining gauge theories, we
compute the spin-0 and spin-2 spectra of the Maldacena–Nuñez and Klebanov–Strassler …

A bstract We revisit the subject of holographic renormalization for asymptotically AdS
spacetimes. For many applications of holography, one has to handle the divergences …