A Note on the Holographic Beta and C Functions

TL;DR

This paper examines the relationship between holographic beta functions and c-functions within AdS/CFT, testing a universal formula and comparing holographic and quantum field theory definitions.

Contribution

It provides checks of the holographic beta and c-function relation and compares different definitions of the c-function in supersymmetric flows.

Findings

The holographic formula relating c and beta functions is consistent with quantum field theory expectations.

Different definitions of the c-function can be compared and contrasted in specific flows.

Holographic and QFT-derived c-functions show agreement in certain supersymmetric cases.

Abstract

The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by a universal formula. We perform some checks of that formula and we compare it with quantum field theory expectations. We discuss alternative definitions of the c-function. In particular, we compare, for a particular supersymmetric flow, the holographic c-function with the central charge computed directly from the two-point function of the stress-energy tensor.