Abstract
We study possible geometries and R-symmetry breaking patterns that lead to globally BPS surface operators in the six dimensional theory. We find four main classes of solutions in different subspaces of and a multitude of subclasses and specific examples. We prove that these constructions lead to supersymmetry preserving observables and count the number of preserved supercharges. We discuss the underlying geometry, calculate their anomalies and present analogous structures for the holographic dual M2-branes in AdS 7 × S 4. We also comment on the dimensional reduction of these observables to line and surface operators in 4D and 5D theories. This rich spectrum of operators is proposed as the simplest and most natural observables of this mysterious theory.
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