Series of Tests of a Constraint on Asymptotically Free Gauge Theories

In 1999 Thomas Appelquist, Andrew G. Cohen, and Martin Schmaltz (ACS) proposed 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 superpotential - the case of Seiberg-dual of $SU(N_{c})$ gauge theory. Here we will verify the conjecture for two new cases - $SO(N_{c})$ and $Sp(2N_{c})$ 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 dynamics 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.