Geometric Holography, the Renormalization Group and the c-Theorem

TL;DR

This paper clarifies the geometric framework of holography in conformal theories and proves a holographic version of the c-theorem using renormalization group flow along null geodesics.

Contribution

It provides a geometric set-up for conformally invariant holography and establishes a holographic c-theorem through RG flow analysis.

Findings

Holographic projection is geometrically clarified.

A holographic c-theorem is proven.

RG flow along null geodesics underpins the theorem.

Abstract

In this paper the whole geometrical set-up giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a holographic version of Zamolodchikov's c-theorem is proven.