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New dualities and misleading anomaly matchings from outer-automorphism twists

New dualities and misleading anomaly matchings from outer-automorphism twists

We study four-dimensional $$ \mathcal{N}=1,\ 2 $$ superconformal theories in class $$ \mathcal{S} $$ obtained by compactifying the 6d $$ \mathcal{N}=\left(2,\ 0\right) $$ theory on a Riemann surface $$ \mathcal{C} $$ with outer-automorphism twist lines. From the pair-of-pants decompositions of $$ \mathcal{C} $$ , we find various dual descriptions for …