Series of tests of a constraint on . . .

... a constraint on the structure of asymptotically-free field theories. This constraint limits the number of degrees of freedom of asymptotically-free gauge theories in the infrared (IR) region relative to those in the ultra-violet (UV) region. In their paper ACS checked various examples, both supersymmetric and non-supersymmetric, but checked only one case of interacting IR fixed point with su-perpotential- the case of Seiberg-dual of SU(Nc) gauge theory. Here we will verify the conjecture for two new cases- SO(Nc) and Sp(2Nc) gauge groups around the Banks-Zaks fixed points. In addition, we subject the ACS inequality to a series of nontrivial tests in theories with conjectured accidental symmetries in the IR and dramatically different dynam-ics caused by superpotential deformations. We start with ADE-type deformations then move on to check three chiral theories by estimating their decoupled invariants from the chiral ring using a-maximization and unitarity considerations. Remarkably, we found no violation of the ACS conjecture