Aspects of the map from Exact RG to Holographic RG in AdS and dS

TL;DR

This paper investigates the connection between Exact RG and Holographic RG in AdS and dS spaces, using a simple quantum mechanical example to illustrate the mapping and its implications for holographic dualities.

Contribution

It demonstrates how a Schrödinger equation with time-dependent mass can be mapped to a harmonic oscillator, providing insights into the RG/holographic correspondence in both AdS and dS contexts.

Findings

Mapping of a Schrödinger equation to a harmonic oscillator.

Analytic continuation links ERG-like equations to dS/CFT.

Insights into the structure of holographic dualities.

Abstract

In earlier work the evolution operator for the exact RG equation was mapped to a field theory in Euclidean AdS. This gives a simple way of understanding AdS/CFT. We explore aspects of this map by studying a simple example of a Schroedinger equation for a free particle with time dependent mass. This is an analytic continuation of an ERG like equation. We show for instance that it can be mapped to a harmonic oscillator. We show that the same techniques can lead to an understanding of dS/CFT too.