Fission, Fusion, and 6D 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.