CFT/CFT interpolating RG flows and the holographic c-function

TL;DR

This paper investigates holographic RG flows between UV and IR fixed points, analyzing the holographic c-function through superpotentials, scattering analogy, and explicit models, confirming its expected properties and IR behavior.

Contribution

It introduces a new scattering-based approach to compute the holographic c-function and provides explicit models demonstrating UV-IR flow behavior.

Findings

The holographic c-function decreases monotonically along flows.

The c-function correctly reproduces IR central charge.

Explicit models validate the theoretical framework.

Abstract

We consider holographic RG flows which interpolate between non-trivial ultra-violet (UV) and infra-red (IR) conformal fixed points. We study the ``superpotentials'' which characterize different flows and discuss their expansions near the fixed points. Then we focus on the holographic $c$-function as defined from the two-point function of the stress-energy tensor. We point out that the equation for the metric fluctuations in the background flow is equivalent to a scattering problem and we use this to obtain an expression for the $c$-function in terms of the associated Jost functions. We propose two explicit models that realize UV-IR flows. In the first example we consider a thin wall separating two AdS spaces with different radii, while in the second one the UV region is replaced with an asymptotically AdS space. We find that the holographic $c$-function obeys the expected properties. In particular it reduces to the correct -- nonzero -- central charge in the IR limit.