(5d RG-flow) Trees in the Tropical Rain Forest

TL;DR

This paper systematically determines the Higgs branches and flavor symmetries of 5d SCFTs derived from 6d theories using a GTP-based approach, elucidating decoupling trees and magnetic quivers.

Contribution

It introduces a GTP-based method to derive magnetic quivers and Higgs branches for entire decoupling trees of 5d SCFTs, including rank 2 cases.

Findings

Computed Higgs branches for large classes of 5d KK-theories.

Determined decoupling trees for all rank 2 5d SCFTs.

Identified non-simply-laced flavor symmetries from magnetic quivers.

Abstract

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 arXiv:2008.05577, 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.