Banks-Zaks fixed point

In quantum chromodynamics (and also $N=1$ superquantum chromodynamics) with massless flavors, if the number of flavors, $N\_f$, is sufficiently small (that is small enough to guarantee asymptotic freedom), 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, then the fixed point is called a 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 $b\_0$ and $b\_1$ are positive constants. Then, there exists a value $g=g\_ast$ such that :
$g\_ast^2\; =\; frac\{b\_0\}\{b\_1\}.$
If we can arrange $b\_0$ to be smaller than $b\_1$, then we have . It follows that the theory in the IR is a conformal, weakly-coupled theory with coupling $g\_ast$.

For the case of QCD the number of flavors, $N\_f$, should lie just below $frac\{11\}\{2\}N\_c$, where $N\_c$ is the number of colors, in order for the Banks-Zaks fixed point to appear.