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

TL;DR

This paper constructs and analyzes a class of 4D $ =1$ superconformal theories derived from M5-branes on complex curves, introducing new building blocks, dualities, and matching central charges with anomaly calculations.

Contribution

It provides a field theoretic construction of theories with $D_N$ blocks, introduces new dualities, and computes operator dimensions and central charges.

Findings

Matching of central charges with anomaly polynomial

Introduction of new $D_N$ building blocks

Exact dimension calculation of heavy operators

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.