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 N $$ \mathcal{N} $$ = 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 C ¯ R , r j j ¯ $$ {\overline{\mathcal{C}}}_{R,r\left(j,\overline{j}\right)} $$ multiplets in the MAD theory for all R, r, j, and j ¯ $$ \overline{j} $$ satisfying R + j ¯ − j + 1 = 0 $$ R+\overline{j}-j+1=0 $$ , 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 / N $$ \mathcal{N} $$ = 2 chiral operator correspondence.

Keywords

• Conformal and W Symmetry
• Extended Supersymmetry
• Supersymmetric Gauge Theory