Chiral theories of class S

TL;DR

This paper constructs and classifies a new class of four-dimensional N=1 superconformal theories derived from six-dimensional theories on orbifolds, revealing dualities and invariance properties through geometric and anomaly analyses.

Contribution

It introduces a systematic classification of chiral quiver gauge theories from 6D origins and demonstrates their duality invariance via Riemann surface constructions and anomaly checks.

Findings

Theories flow to the same IR fixed point based on Riemann surface equivalence.

Explicit anomaly and central charge calculations confirm duality invariance.

Classification of building blocks for pair-of-pants decompositions.

Abstract

We study a class of four-dimensional N=1 superconformal field theories obtained from the six-dimensional (1,0) theory, on M5-branes on C^2/Z_k orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge theories whose matter contents are chiral. We classify the building blocks associated to pairs-of-pants, and study the gauging of them as the gluing of punctures. The Riemann surface picture makes the duality invariance of the resulting quiver theories manifest: the theories associated to the same Riemann surface flow to the same nontrivial infrared fixed point. We explicitly check this from the 't Hooft anomalies of the global symmetries and central charges.