On 5D SCFTs and their BPS quivers. Part I: B-branes and brane tilings

We study the spectrum of BPS particles on Coulomb branch five-dimensional superconformal field theories (5d SCFTs) compactified a circle. By engineering these in M-theory ${\mathbf X} \times S^1 $, for X}$ an isolated Calabi-Yau threefold singularity, we naturally identify category 5d theory circle with derived coherent sheaves resolution X}$. It follows that can be studied terms quivers, which are fractional-brane quivers singularity generalize well-studied 4d $\mathcal{N}{=}2$ gauge obtained from so-called geometric limits. interplay between and detail. particularly focus examples when is toric case quiver given brane tiling. For instance, $Y^{p,q}$ tiling gives $SU(p)_q$ theory. present conjecture about structure spectra wide class models, test simple $SU(2)_0$ (more precisely, $E_1$ SCFT). also argue UV dualities realized mutation sequences turn interpreted as autoequivalences category.