A note on the holographic beta and C functions

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 the formula c = -2c beta(a)beta(b)G(ab), where G(ab) is the metric of the kinetic term of the supergravity scalars. In particular, the metric in the space of couplings is f(ab) = 2cG(ab). We perform some checks of that result and we compare it with the 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. (C) 2000 Elsevier Science B.V. All rights reserved.