A Banks-Zaks fixed point is an IR-stable CFT describing long-distance behavior of QCD for certain parameters. The Lagrangian of QCD is $$\mathcal L= \sum_a \bar\psi_a (i \gamma\partial - m_a ) \psi_a - \frac 1 4 F^2$$ where color and spacetime indices have been suppressed. The flavor index $a$ runs over $N_f$ flavors of fermions.

This theory is asymptotically free (i.e., has a UV-stable fixed point) for $N_f < \frac {33} 2$. For $N_f$ just below that threshold, an IR-stable fixed point is visible in perturbation theory if the fermions are taken to be massless. This fixed point has been found to extend down at least to $N_f \sim 12$ in lattice studies.

Other theories can have Banks-Zaks fixed points, like SQCD.

Here are some lattice studies: https://arxiv.org/abs/0712.0609, https://arxiv.org/abs/0904.4662.

• Wikipedia
• https://arxiv.org/pdf/0905.4752.pdf