S Parameter in the Holographic Walking/Conformal Technicolor

We explicitly calculate the S parameter in entire parameter space of the holographic walking/conformal technicolor (W/C TC), based on the deformation of the holographic QCD by varying the anomalous dimension from gamma(m) similar or equal to 0 through gamma(m) similar or equal to 1 continuously. The S parameter is given as a positive monotonic function of which is fairly insensitive to gamma(m) and continuously vanishes as S similar to xi(2) -> 0 when xi -> 0, where is the vacuum expectation value of the bulk scalar field at the infrared boundary of the 5th dimension z = z(m) and is related to the mass of (techni-) rho meson (M-rho) and the decay constant (f(pi)) as xi similar to f(pi)z(m) similar to f(pi)/M-rho for xi << 1. However, although xi is related to the techni-fermion condensate < TT >, we find no particular suppression of and hence of S due to large gamma(m), based on the correct identification of the renormalization-point dependence of <(T) over barT > in contrast to the literature. Then we argue possible behaviors of f(pi)/M-rho as <(T) over barT > -> 0 near the conformal window characterized by the Banks-Zaks infrared fixed point in more explicit dynamics with gamma(m) similar or equal to 1. It is a curious coincidence that the result from ladder Schwinger-Dyson and Bethe-Salpeter equations well fits in the parameter space obtained in this paper. When f(pi)/M-rho -> 0 is realized, the holography suggests a novel possibility that f(pi) vanishes much faster than the dynamical mass m does.