On the Protected Spectrum of the Minimal Argyres-Douglas Theory

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 $\mathcal{N}=2$ 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 $\mathcal{N}=1\subset \mathcal{N}=2$ 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 $\mathcal{N}=2$ Abelian gauge theory. In the language of superconformal representation theory, this leaves only the spectrum of the poorly understood ${\bar{\mathcal{C}}}_{R,r(j,\bar{j})}$ multiplets to be determined. Our second result sheds light on these observables: we find an exact closed-form answer for the number of ${\bar{\mathcal{C}}}_{0,r(j,0)}$ 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 $\mathcal{N}=2$ Abelian gauge theory. These results motivate a conjecture on the full local operator algebra of the MAD theory.

34 pages and 2 appendices; v2: references added and typos corrected

References in corpus (10)

• Supersymmetric gauge theories with decoupled operators and chiral ring stability
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• Higher Form Symmetries of Argyres-Douglas Theories
• Constraints on Chiral Operators in N=2 SCFTs
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Goldstinos, Supercurrents and Metastable SUSY Breaking in N=2 Supersymmetric Gauge Theories
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Supersymmetry breaking deformations and phase transitions in five dimensions
• OPE coefficients in Argyres-Douglas theories
• A study of N =1 SCFT derived from N =2 SCFT: index and chiral ring

Cited by in corpus (2)

• Exact Operator Map from Strong Coupling to Free Fields: Beyond Seiberg-Witten Theory
• Argyres-Douglas Avatars of Coulomb Branch Physics