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 [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.
Highlights
Our understanding of 5d superconformal field theories (SCFTs) derives in large part from our ability to construct and study these theories in string theory. 5d N = 1 SCFTs can arise in M-theory by compactification on a canonical Calabi-Yau three-fold singularity, or in type IIB string theory as the world-volume theory of a 5-brane-web
We identify the flavor symmetry algebras from the magnetic quivers, including non--laced flavor symmetries
A precise correspondence of the deformation space of the Calabi-Yau singularity and the Higgs branch (HB) of the associated 5d SCFT has only been achieved for singularities that can be realized as strictly convex toric polygons [31, 32] and, recently, for isolated hyper-surface singularities [33]
Summary
We show how the geometric implementation of decoupling hyper-multiplets by performing flop transitions [16] is realized as a flop of the corresponding matter curve in the pGTP, directly generalizing the application for toric models in [26] Together, these operations clearly allow us to reach any pGTP (i.e. 5d gauge theory) in a given descendant tree and take the strong-coupling limit to obtain the corresponding GTP (SCFT). In particular we will give rules how to identify certain non- laced flavor symmetries as well, like g2
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