Behavior of the S Parameter in the Crossover Region Between Walking and QCD-Like Regimes of an SU(N) Gauge Theory

We consider a vectorial, confining SU(N) gauge theory with a variable number, $N_f$, of massless fermions transforming according to the fundamental representation. Using the Schwinger-Dyson and Bethe-Salpeter equations, we calculate the $S$ parameter in terms of the current-current correlation functions. We focus on values of $N_f$ such that the theory is in the crossover region between the regimes of walking behavior and QCD-like (non-walking) behavior. Our calculations indicate that the contribution to $S$ from a given fermion decreases as one moves from the QCD-like to the walking regimes. The implications of this result for technicolor theories are discussed.