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

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

2001-12-18

arxiv.org/abs/hep-th/0112150v3

JHEP 0204:027,2002

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, discussion at the end of sec. 3 and sec. 4.1 changed

Scientific paper

10.1088/1126-6708/2002/04/027

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.

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