Small deformation of a simple $\mathcal{N}=2$ superconformal theory

We study an interesting relevant deformation of the simplest interacting $\mathcal{N}=2$ superconformal field theory (SCFT)—the original Argyres-Douglas (AD) theory. We argue that, although this deformation is not strictly speaking Banks-Zaks–like (certain operator dimensions change macroscopically), there are senses in which it constitutes a mild deformation of the parent AD theory: the exact change in the $a$ anomaly is small and is essentially saturated at one loop. Moreover, contributions from IR operators that have a simple description in the UV theory reproduce a particular limit of the IR index to a remarkably high order. These results lead us to conclude that the IR theory is an interacting $\mathcal{N}=1$ SCFT with particularly small $a$ and $c$ central charges and that this theory sheds some interesting light on the spectrum of its AD parent. Our results also lead us to the conclusion that the theory spaces emanating from some of the simplest $\mathcal{N}=1$ gauge theories may be richer than anticipated.