Holographic renormalization by Hamilton-Jacobi formulation with generated ansatz

TL;DR

This paper introduces a Hamilton-Jacobi based method for holographic renormalization that generates exact counterterm ansatzes, simplifying the process compared to traditional Fefferman-Graham expansion methods.

Contribution

It develops an alternative holographic renormalization approach using Hamilton-Jacobi formulation that produces exact counterterm ansatzes, enhancing efficiency and applicability.

Findings

Successfully applied to various holographic models

Consistently performs well in removing divergences

Simplifies the renormalization process

Abstract

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 holographic renormalization is based on the Fefferman-Graham expansion, which is strict and universal but technically cumbersome. To improve the technique, different methods have been proposed. Here we develop an alternative approach to holographic renormalization based on the Hamilton-Jacobi formulation of gravity. Compared to previous approaches, its distinguishing feature is the generation of exact ansatz of counterterms. We apply this approach to several typical holographic models, which consistently performs well.