On the Protected Spectrum of the Minimal Argyres-Douglas Theory
arXiv:2205.07930 · doi:10.1007/JHEP08(2022)132
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 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 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 quantum numbers and the vanishing of a finite number of states, the MAD FCS is isospectral to the FCS of the free Abelian gauge theory. In the language of superconformal representation theory, this leaves only the spectrum of the poorly understood multiplets to be determined. Our second result sheds light on these observables: we find an exact closed-form answer for the number of multiplets, for any and , 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 Abelian gauge theory. These results motivate a conjecture on the full local operator algebra of the MAD theory.
arXiv comment34 pages and 2 appendices; v2: references added and typos corrected
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