In quantum chromodynamics (and also N = 1 superquantum chromodynamics) with massless flavors, if the number of flavors, Nf, is sufficiently small (i.e. small enough to guarantee asymptotic freedom, depending on the number of colors), the theory can flow to an interacting conformal fixed point of the renormalization group. If the value of the coupling at that point is less than one (i.e. one can perform perturbation theory in weak coupling), then the fixed point is called a Banks–Zaks fixed point. The existence of the fixed point was first reported by William E. Caswell in 1974, and later used by Banks and Zaks in their analysis of the phase structure of vector-like gauge theories with massless fermions. For this reason one also justifiably finds references to a Caswell-Banks–Zaks fixed point.
More specifically, suppose that we find that the beta function of a theory up to two loops has the form
where
If we can arrange
For the case of a non-Abelian gauge theory with gauge group
where
where the lower bound comes from requiring