A note on holographic renormalization for non-conformal branes by recursion

TL;DR

This paper reviews holographic renormalization for non-conformal branes using Hamilton-Jacobi formalism, providing tools for the holographic dictionary and new technical results for $Dp$-branes with $p<5$ in Einstein-Maxwell-dilaton theory.

Contribution

It introduces a recursive algorithm for holographic renormalization of non-conformal branes, extending previous methods to $Dp$-branes with $p<5$ in Einstein-Maxwell-dilaton models.

Findings

Developed a recursive algorithm for Hamilton-Jacobi equations in holography.

Provided new technical results for $Dp$-branes with $p<5$.

Enhanced tools for computing the holographic dictionary for non-conformal branes.

Abstract

We review holographic renormalization for non-conformal branes using the Hamilton-Jacobi formalism. We provide the tools required for the computation of the holographic dictionary, while we present some marginally new technical results regarding holographic renormalization for $Dp$-branes, $p<5$, for Einstein-Maxwell theory coupled to a dilaton. The computations are based on a recursive algorithm by Papadimitriou, that solves the radial Hamilton-Jacobi equation in the asymptotic boundary of the bulk. This paper is a short version of the Master thesis of the author written in 2014 at the Instituto de F\'isica Te\'orica, UAM, Madrid.