On the protected spectrum of the minimal Argyres-Douglas theory

Abstract

Abstract Despite the power of supersymmetry, finding exact closed-form expressions for the protected operator spectra of interacting superconformal field theories (SCFTs) is difficult. In this paper, we take a step towards a solution for the “simplest” interacting 4D $$ \mathcal{N} $$ N = 2 SCFT: the minimal Argyres-Douglas (MAD) theory. We present two results that go beyond the well-understood Coulomb branch and Schur sectors. First, we find the exact closed-form spectrum of multiplets containing operators that are chiral with respect to any $$ \mathcal{N} $$ N = 1 ⊂ $$ \mathcal{N} $$ N = 2 superconformal subalgebra. We argue that this “full” chiral sector (FCS) is as simple as allowed by unitarity for a theory with a Coulomb branch and that, up to a rescaling of U(1)r quantum numbers and the vanishing of a finite number of states, the MAD FCS is isospectral to the FCS of the free $$ \mathcal{N} $$ N = 2 Abelian gauge theory. In the language of superconformal representation theory, this leaves only the spectrum of the poorly understood $$ {\overline{\mathcal{C}}}_{R,{r}_{\left(j,\overline{j}\right)}} $$ C ¯ R , r j j ¯ multiplets to be determined. Our second result sheds light on these observables: we find an exact closed-form answer for the number of $$ {\overline{\mathcal{C}}}_{0,{r}_{\left(j,0\right)}} $$ C ¯ 0 , r j 0 multiplets, for any r and j, in the MAD theory. We argue that this sub-sector is also as simple as allowed by unitarity for a theory with a Coulomb branch and that there is a natural map to the corresponding sector of the free $$ \mathcal{N} $$ N = 2 Abelian gauge theory. These results motivate a conjecture on the full local operator algebra of the MAD theory.