====== Banks-Zaks fixed point ======

{{tag>4d}}

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.



===== Lattice studies =====

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

===== External links =====

  * [[https://en.wikipedia.org/wiki/Banks%E2%80%93Zaks_fixed_point|Wikipedia]]
  * [[https://arxiv.org/pdf/0905.4752.pdf]]