Argyres-Douglas avatars of Coulomb branch physics

Abstract

Abstract We study ultraviolet (UV) incarnations of deep infrared (IR) physics on the Coulomb branch of the simplest interacting 4D $$ \mathcal{N} $$ 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 $$ {\overline{\mathcal{C}}}_{R,r\left(j,\overline{j}\right)} $$ C ¯ R , r j j ¯ multiplets in the MAD theory for all R, r, j, and $$ \overline{j} $$ j ¯ satisfying $$ R+\overline{j}-j+1=0 $$ R + 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 / $$ \mathcal{N} $$ N = 2 chiral operator correspondence.