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{s}mathfrak{u}(2)to {mathfrak{g}}_{mathrm{flav}} for {mathfrak{g}}_{mathrm{flav}} a flavor symmetry also points the way to a classification of 6D RG flows.
Highlights
Perhaps surprisingly, this issue is tractable for 6D superconformal field theories (SCFTs)
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”
While we have not performed an exhaustive sweep over every 6D SCFT from the classification of reference [9], we already see that outlier theories exhibit some structure, and within the corresponding patterns, we find no counterexamples to the claim that all 6D SCFTs are products of either a single fission operation or fission and a further fusion operation
Summary
We introduce two general operations for 6D SCFTs which we refer to as fission and fusion. Reference [9] classified 6D SCFTs by determining all possible F-theory backgrounds which can generate a 6D SCFT This was achieved by first listing all configurations of simultaneously contractible curves, and listing all possible elliptic fibrations over each corresponding base. One reaches an “endpoint configuration” in which no −1 curves remain, that is to say, all remaining curves have self-intersection −m with m > 1 The structure of these endpoint configurations were completely classified in reference [7], and have intersection pairings which are natural generalizations of the ADE series associated with Kleinian singularities. Our plan in the remainder of this section will be to characterize the geometric content of RG flows for 6D SCFTs. We begin with a discussion of tensor branch and Higgs branch deformations, and turn to the specific case of fission and fusion operations
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