Series of Tests of a Constraint on Asymptotically Free Gauge Theories

We revisit the constraint proposed by T. Appelquist, A. G. Cohen, and M. Schmaltz (ACS) on asymptotically free field theories, which relates the number of infrared (IR) degrees of freedom to those in the ultraviolet (UV). The original ACS analysis examined several examples—both supersymmetric and non-supersymmetric—and identified only one interacting IR fixed point with a superpotential: Seiberg dual of an SU(Nc) gauge theory. Here, we extend their analysis to SO(Nc) and Sp(2Nc) gauge groups near Banks–Zaks fixed points. We further test the ACS inequality in theories featuring conjectured accidental IR symmetries and nontrivial superpotential deformations. Beginning with ADE-type deformations, we then investigate three chiral theories by estimating decoupled chiral-ring invariants using a-maximization and unitarity bounds. In all cases, we find no violation of the ACS conjecture.