Description
4d CFTs with identical central charges have a variety of novel physical properties, even when there is not enhanced N=3 or N=4 supersymmetry. I introduce a construction of N=1 and N=2 SCFTs with a=c (from Argyres--Douglas building blocks). I point out interesting features such as the behavior of the Schur index, and the lessons that we can learn about the Higgs branch Hilbert series and Hall--Littlewood index of generic class S theories. Next, I will discuss dualities between these non-Lagrangian a=c theories and Lagrangian theories, including where there is supersymmetry enhancement. Finally, I comment on the existence of a mixed-anomaly between one-form and axial symmetries in these a=c theories, and how that can constrain the infrared behavior of such theories after superpotential deformation.
