$\mathcal{N}=1$ superconformal theories with $D_N$ blocks

Abstract

We study the chiral ring of four-dimensional superconformal field theories obtained by wrapping M5-branes on a complex curve inside a Calabi-Yau three-fold. We propose a field theoretic construction of all the theories found by Bah, Beem, Bobev and Wecht by introducing new building blocks, and prove several $\mathcal{N}=1$ dualities featuring the latter. We match the central charges with those computed from the M5-brane anomaly polynomial, perform the counting of relevant operators and analyze unitarity bound violations. As a byproduct, we compute the exact dimension of "heavy operators" obtained by wrapping an M2-brane on the complex curve.

45 pages, 17 figures; v2: typos fixed, minor changes, references added, conclusions added, version published in Phys. Rev. D

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• Structure of Anomalies of 4d SCFTs from M5-branes, and Anomaly Inflow
• 4d N=1 from 6d N=(1,0) on a torus with fluxes
• Wrapped Branes and Punctured Horizons
• Star shaped quivers with flux
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• The Geometry of SUSY Enhancement
• Rank $Q$ E-String on Spheres with Flux
• Aspects of 4d supersymmetric dynamics and geometry