Attractive holographic $c$-functions

TL;DR

This paper constructs a bulk-based holographic c-function in ${ m AdS}$ geometries, interpolating between UV and IR conformal fixed points, revealing insights into RG flows between different-dimensional CFTs.

Contribution

It introduces a novel holographic c-function derived from the attractor mechanism in ${ m AdS}$ supergravity, connecting different-dimensional CFTs at fixed points.

Findings

The c-function smoothly interpolates between UV and IR fixed points.

It is expressed purely in terms of bulk supergravity quantities.

The c-function links two different dimensional CFTs at stable fixed points.

Abstract

Using the attractor mechanism for extremal solutions in ${\cal N}=2$ gauged supergravity, we construct a $c$-function that interpolates between the central charges of theories at ultraviolet and infrared conformal fixed points corresponding to anti-de Sitter geometries. The $c$-function we obtain is couched purely in terms of bulk quantities and connects two different dimensional CFTs at the stable conformal fixed points under the RG flow.