(5d RG-flow) trees in the tropical rain forest

5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in [1], which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers and their Hasse diagrams. The decoupling in the GTP description is straightforward, and generalizes the standard flop transitions of curves in toric polygons. We apply this approach to a large class of 5d KK-theories, and compute the Higgs branches for their descendants. In particular we determine the decoupling tree for all rank 2 5d SCFTs. For each tree, we also identify the flavor symmetry algebras from the magnetic quivers, including non-simply-laced flavor symmetries.

Automated summary

This paper investigates the generation process of 5d SCFTs from 6d SCFTs, including the decoupling of hypermultiplet matter, RG-flow, and the construction of decoupling trees. By using the approach of generalized toric polygons, magnetic quivers and Hasse diagrams of 5d SCFTs are systematically derived, and the Higgs branches of various 5d KK-theories and their descendants are computed.