Non-Perturbative Explorations of Chiral Rings in 4d N=2 SCFTs

Abstract

We study the conditions under which 4d N = 2 superconformal field theories (SCFTs) have multiplets housing operators that are chiral with respect to an N = 1 subalgebra. Our main focus is on the set of often-ignored and relatively poorly understood B¯ representations. These multiplets typically evade direct detection by the most popular non-perturbative 4d N = 2 tools and correspondences. In spite of this fact, we demonstrate the ubiquity of B¯ multiplets and show they are associated with interesting phenomena. For example, we give a purely algebraic proof that they are present in all local unitary N > 2 SCFTs. We also show that B¯ multiplets exist in N = 2 theories with rank greater than one and a conformal manifold or a freely generated Coulomb branch. Using recent topological quantum field theory results, we argue that certain B¯ multiplets exist in broad classes of theories with the Z2-valued ’t Hooft-Witten anomaly for Sp(N) global symmetry. Motivated by these statements, we then study the question of when B¯ multiplets exist in rank-one SCFTs with exactly N = 2 SUSY and vanishing ’t Hooft-Witten anomaly. We conclude with various open questions.