Coulomb branches of vacua are the most universal moduli spaces that arise in local unitary interacting 4d \( \mathcal{N} \) = 2 superconformal field theories (SCFTs). In these theories, 1/2-BPS primaries parameterize the Coulomb branches and form (anti-)chiral rings. We define the notion of a Coulomb branch operator algebra, \( {\mathcal{A}}_{\mathcal{C}} \) , that contains these chiral and anti-chiral rings along with infinitely many more operators and products that are less protected by supersymmetry. Using a universal symmetry, \( \mathcal{I}\cong {\mathbb{Z}}_2 \) , that arises from studying the superconformal group, we give \( \mathcal{I} \) selection rules for \( {\mathcal{A}}_{\mathcal{C}} \) and, more generally, for arbitrary products in the local operator algebra of any 4d \( \mathcal{N} \) = 2 SCFT. Defining the notion of a “Coulombic” SCFT, we propose explanations for certain phenomena in a 4d/2d correspondence involving 4d \( \mathcal{N} \) = 2 theories and 2d vertex operator algebras. Finally, by considering deformations of \( \mathcal{I} \) , we explore the case of \( \mathcal{N} \) > 2 SCFTs.
