Classification of Argyres-Douglas theories from M5 branes

We obtain a large class of new four-dimensional Argyres-Douglas theories by classifying irregular punctures for the six-dimensional (2, 0) superconformal theory of ADE type on a sphere. Along the way, we identify the connection between the Hitchin system and threefold singularity descriptions of the same Argyres-Douglas theory. Other constructions such as taking degeneration limits of the irregular puncture, adding an extra regular puncture, and introducing outer-automorphism twists are also discussed. Later we investigate various features of these theories including their Coulomb branch spectrum and central charges.