Compactifications of 6d N $$ \mathcal{N} $$ = (1, 0) SCFTs with non-trivial Stiefel-Whitney classes

Abstract

Abstract We consider compactifications of very Higgsable 6d N $$ \mathcal{N} $$ =(1, 0) SCFTs on T 2 with non-trivial Stiefel-Whitney classes (or equivalently ’t Hooft magnetic fluxes) introduced for their flavor symmetry groups. These systems can also be studied as twisted S 1 compactifications of the corresponding 5d theories. We deduce various properties of the resulting 4d N $$ \mathcal{N} $$ =2 SCFTs by combining these two viewpoints. In particular, we find that all 4d rank-1 N $$ \mathcal{N} $$ =2 SCFTs with a dimension-6 Coulomb branch operator with flavor symmetry e $$ \mathfrak{e} $$ 8, u s p $$ \mathfrak{u}\mathfrak{s}\mathfrak{p} $$ (10), s u $$ \mathfrak{s}\mathfrak{u} $$ (4) and s u $$ \mathfrak{s}\mathfrak{u} $$ (3) can be uniformly obtained by starting from a single-tensor theory in 6d. We also have a mostly independent appendix where we propose a rule to determine the Coulomb branch dimensions of 4d N $$ \mathcal{N} $$ =2 theories obtained by T 2 compactifications of 6d very Higgsable theories with and without Stiefel-Whitney twist.

Keywords

• Field Theories in Higher Dimensions
• Supersymmetric Gauge Theory
• String Duality