A 5d perspective on the compactifications of 6d SCFTs to 4d $$ \mathcal{N} $$ = 1 SCFTs

Compactifying 6d superconformal field theories (SCFTs) to 4d $\mathcal{N}=1$ on two-punctured spheres (tubes) and tori with flux is realized using duality domain walls in 5d Kaluza-Klein (KK) theories, which are usually denoted by $flux$ $domain$ $walls$. We revisit this construction study it detail from the perspective, specifically rephrasing box graph description of extended Coulomb branch phases theories. This perspective could be helpful understanding how equivalently realize models geometric engineering M-theory. Along way, we show recover various properties such as associated wall configurations presence a $\mathfrak{u}(1)$ global symmetry theory descending KK tube, broken discrete subgroup torus. demonstrate all these ideas rank 1 E-string theory.