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We systematically analyse 5d superconformal field theories (SCFTs) obtainedby dimensional reduction from 6d $\mathcal{N}=(1,0)$ SCFTs. Such theories havea realization as M-theory on a singular Calabi-Yau threefold, from which wedetermine the so-called combined fiber diagrams (CFD) introduced inarXiv:1906.11820, arXiv:1907.05404, arXiv:1909.09128. The CFDs are graphs thatencode the superconformal flavor symmetry, BPS states, low energy descriptions,as well as descendants upon flavor matter decoupling. To obtain a 5d SCFT from6d, there are two approaches: the first is to consider a circle-reductioncombined with mass deformations. The second is to circle-reduce and decouple anentire gauge sector from the theory. The former is applicable e.g. for veryHiggsable theories, whereas the latter is required to obtain a 5d SCFT from anon-very Higgsable 6d theory. In the M-theory realization the latter casecorresponds to decompactification of a set of compact surfaces in theCalabi-Yau threefold. To exemplify this we consider the 5d SCFTs that descendfrom non-Higgsable clusters and non-minimal conformal matter theories. Finally,inspired by the quiver structure of 6d theories, we propose a gluingconstruction for 5d SCFTs from building blocks and their CFDs.

5d SCFTs from Decoupling and Gluing