Fission, Fusion, and 6D RG Flows

TL;DR

This paper demonstrates that all known 6D superconformal field theories can be systematically constructed from basic progenitors through processes called fission and fusion, revealing a unified classification scheme.

Contribution

It introduces a novel iterative framework using fission and fusion to generate and classify all known 6D SCFTs based on group theoretic data.

Findings

All 6D SCFTs can be obtained via fission and fusion processes.

A streamlined labeling scheme for 6D SCFTs based on group theory.

Partial ordering of homomorphisms suggests a classification of RG flows.

Abstract

We show that all known 6D SCFTs can be obtained iteratively from an underlying set of UV progenitor theories through the processes of "fission" and "fusion." Fission consists of a tensor branch deformation followed by a special class of Higgs branch deformations characterized by discrete and continuous homomorphisms into flavor symmetry algebras. Almost all 6D SCFTs can be realized as fission products. The remainder can be constructed via one step of fusion involving these fission products, whereby a single common flavor symmetry of decoupled 6D SCFTs is gauged and paired with a new tensor multiplet at the origin of moduli space, producing an RG flow "in reverse" to the UV. This leads to a streamlined labeling scheme for all known 6D SCFTs in terms of a few pieces of group theoretic data. The partial ordering of continuous homomorphisms $\mathfrak{su}(2) \rightarrow \mathfrak{g}_{\text{flav}}$ for $\mathfrak{g}_{\text{flav}}$ a flavor symmetry also points the way to a classification of 6D RG flows.