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We consider holographic RG flows which interpolate between non-trivialultra-violet (UV) and infra-red (IR) conformal fixed points. We study the``superpotentials'' which characterize different flows and discuss theirexpansions near the fixed points. Then we focus on the holographic $c$-functionas defined from the two-point function of the stress-energy tensor. We pointout that the equation for the metric fluctuations in the background flow isequivalent to a scattering problem and we use this to obtain an expression forthe $c$-function in terms of the associated Jost functions. We propose twoexplicit models that realize UV-IR flows. In the first example we consider athin wall separating two AdS spaces with different radii, while in the secondone the UV region is replaced with an asymptotically AdS space. We find thatthe holographic $c$-function obeys the expected properties. In particular itreduces to the correct -- nonzero -- central charge in the IR limit.Comment: 20 pages, discussion at the end of sec. 3 and sec. 4.1 change

CFT/CFT interpolating RG flows and the holographicc-function