Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs

Abstract

Many interesting phenomena in quantum field theory such as dualities and symmetry enhancements can be understood using higher dimensional constructions. In this paper, we study compactifications of the rank $1$ $5d$ Seiberg $E_{N_f+1}$ SCFTs to $3d$ on Riemann surfaces of genus $g>1$. We rely on the recent progress in the study of compactifications of $6d$ SCFTs to $4d$ and torus compactifications of $5d$ SCFTs to conjecture $3d$ $\mathcal{N}=2$ theories corresponding to the reduction of said $5d$ SCFTs on three punctured spheres. These can then be used to build $3d$ $\mathcal{N}=2$ models corresponding to compactifications on more general surfaces. The conjectured theories are tested by comparing their properties against those expected from the compactification picture.