loop corrections and non-perturbative effects are incorporated due the presence of dressed, field-dependent propagators $(\Gamma_k^{(2)}+R_k)^{-1}$. Flow equations for propagators or higher order $n$-point functions are obtained by taking appropriate functional derivatives of . Despite its nature as an exact equation, most practical applications require an Ansatz for the scale-dependent effective action. Therefore, identifying the operators that carry the relevant physical information is of utmost importance for any quantitatively reliable solution of the flow equation (\[eq:floweq\]).

Four-fermi interactions, e.g. in the scalar channel with coupling $\lambda_{(\bar\psi\psi)^2}$, are created dynamically from two-gluon exchange box diagrams that are proportional to $\alpha_s^2$. The back-coupling of these four-fermi interactions on the system is suppressed by additional powers of $\alpha_s^2$, for example its contributions to the four-fermi system is of order $\alpha_s^4$. However, as the strong running coupling, $\alpha_s$, becomes large close to $\Lambda_{\text{QCD}}$, the suppression of the four-fermi interactions is overcome and they start to grow large. As it becomes sufficiently large, the four-fermi dynamics eventually become dominant and lead to a four-fermi resonance. This resonance corresponds to the light pions as pseudo–Nambu-Goldstone modes in the spontaneously broken phase. For even smaller momentum scales, quark interactions exhibit dominant scatterings of these resonant momentum channels. Hence, 