Tinkertoys for Gaiotto Duality

TL;DR

This paper develops a classification method for N=2 superconformal theories derived from 6D SCFTs compactified on Riemann surfaces, revealing numerous new S-dualities between different types of theories.

Contribution

It provides an explicit classification of building blocks for these theories, including spheres and cylinders, up to N=5 and for various families, enabling systematic discovery of dualities.

Findings

Classified 3-punctured spheres and cylinders for N up to 5.

Discovered new S-dualities between Lagrangian and non-Lagrangian theories.

Established a framework for understanding Gaiotto duality through geometric decompositions.

Abstract

We describe a procedure for classifying N=2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A_{N-1} SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N=5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian N=2 SCFTs.