Argyres-Douglas Avatars of Coulomb Branch Physics

Abstract: We study ultraviolet (UV) incarnations of deep infrared (IR) physics on the Coulomb branch of the simplest interacting 4D $\mathcal{N}=2$ superconformal field theory: the minimal Argyres-Douglas (MAD) theory. One of the most basic properties of the Coulomb branch is an emergent infinite-dimensional higher-spin symmetry. While the MAD theory is interacting and therefore does not have such a symmetry, we find UV operators that encode the emergent complex higher-spin symmetry on the Coulomb branch. Moreover, we show that cousins of these UV operators give rise to cousins of the IR higher-spin multiplets. In terms of superconformal representation theory, we are led to a conjecture on the exact spectrum of $\bar{\mathcal{C}}_{R,r(j,\bar j)}$ multiplets in the MAD theory for all $R$, $r$, $j$, and $\bar j$ satisfying $R+\bar j -j+1=0$, thereby making progress towards a full characterization of the protected spectrum. Along the way, we give a geometrical interpretation of these operators and include them in an extension of the Coulomb branch / $\mathcal{N}=2$ chiral operator correspondence.