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--- banks_zaks_fixed_point [2021/05/08 23:48]
Scott Lawrence [Banks-Zaks fixed point]
+++ banks_zaks_fixed_point [2021/05/10 05:34] (current)
Scott Lawrence [Banks-Zaks fixed point]
@@ Line 3: / Line 3: @@
 {{tag>4d}}
-The Banks-Zaks fixed point is an IR-stable CFT describing long-distance behavior of QCD for certain parameters. The Lagrangian of QCD is
+A Banks-Zaks fixed point is an IR-stable CFT describing long-distance behavior of QCD for certain parameters. The Lagrangian of QCD is
 \[
 \mathcal L=
-\bar\psi_a (i \gamma\partial - m ) \psi_a - \frac 1 4 F^2
+\sum_a \bar\psi_a (i \gamma\partial - m_a ) \psi_a - \frac 1 4 F^2
 \]
-where color and spacetime indices have been surpressed. The flavor index $a$ runs over
+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.

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