Related papers: Holographic Trace Anomaly and Local Renormalizatio…
The holographic renormalization group (RG) is reviewed in a self-contained manner. The holographic RG is based on the idea that the radial coordinate of a space-time with asymptotically AdS geometry can be identified with the RG flow…
The Weyl anomaly in the Holographic Renormalisation Group as implemented using Hamilton-Jacobi language is studied in detail. We investigate the breakdown of the descent equations in order to isolate the Weyl anomaly of the dual field…
A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg…
We give a prescription for calculating the holographic Weyl anomaly in arbitrary dimension within the framework based on the Hamilton-Jacobi equation proposed by de Boer, Verlinde and Verlinde. A few sample calculations are made and shown…
In AdS/CFT corresponding, the UV divergence of generating functional on the field theory can be removed as the IR divergence in the gravity. This geometric process is well known as holographic renormalization. The standard method of…
We find the Holographic Renormalization Group equations for the holographic duals of generic gravity theories coupled to form fields and spin-1/2 fermions. Using Hamilton-Jacobi theory we discuss the structure of Ward identities, anomalies,…
We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence. Starting with a $(d+1)$-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG…
Recently, a practical approach to holographic renormalization has been developed based on the Hamilton-Jacobi formulation. Using a simple Einstein-scalar theory, we clarify that this approach does not conflict with the Hamiltonian…
We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses…
A quantum-field theoretical interpretation is given to the holographic RG equation by relating it to a field-theoretical local RG equation which determines how Weyl invariance is broken in a quantized field theory. Using this approach we…
The Holographic Wess--Zumino (HWZ) consistency conditions are shown through a step by step mapping of renormalization group flows to Hamiltonian systems, to lead to the Holographic anomaly. These conditions codify how the energy scale, when…
Holographic model of massive scalar field with its self-interaction $\lambda\phi^n$ in AdS space is able to give a logarithmic scale dependence to marginal multi trace deformation couplings on its dual conformal field theory, where…
This paper is an extended version of our short letter on a new proposal for holographic boundary conformal field, i.e., BCFT. By using the Penrose-Brown-Henneaux (PBH) transformation, we successfully obtain the expected boundary Weyl…
We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric…
We use the relation between certain diffeomorphisms in the bulk and Weyl transformations on the boundary to build the conformal structure of the metric in the presence of matter in the bulk. We explicitly obtain the conformal anomaly in any…
We discuss various issues related to the understanding of the conformal anomaly matching in CFT from the dual holographic viewpoint. First, we act with a PBH diffeomorphism on a generic 5D RG flow geometry and show that the corresponding…
From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We,…
We study holographic renormalization and the variational problem in four-dimensional Einstein gravity coupled to a self-interacting scalar field in asymptotically AdS spacetimes with mixed, designer-gravity boundary conditions. For static…
We provide a general algorithm for constructing the holographic dictionary for any asymptotically locally Lifshitz background, with or without hyperscaling violation, and for any values of the dynamical exponents $z$ and $\theta$, as well…
We adapt the Hamilton-Jacobi method of holographic renormalization to scalar field theories in Minkowski spacetime with scattering boundary conditions. The approach yields a flat-space holographic dictionary in which the expectation value…