Natural Anomaly Matching

In a large class of chiral gauge theories in four dimensions it was found that certain natural assumption about the bifermion condensates leads to the infrared effective theory where the 't Hooft anomaly matching conditions are satisfied in an entirely evident fashion, without need of verifying arithmetic equations. This is due to the fact that in these systems, characterized by dynamical color (and flavor) symmetry breaking, the quantum numbers and multiplicities of the low-energy massless fermions match exactly those of the fermions in the UV theory which do not condense and remain massless, with respect to the unbroken symmetries. This means also that the stronger constraints following from the matching request of mixed anomalies involving certain generalized 1-form center symmetries, as well as some global anomalies such as Witten's $SU(2)$ anomaly, are all fully satisfied. It is the aim of this note to clarify better the working of this phenomenon (which we call Natural Anomaly Matching), correct some earlier statements made about it, and illustrate it further with a few new examples.