Generalized Instanton Symmetry Induced by Monopoles

We point out that there exists a generalization of instanton symmmetry in the Coulomb phase of 5d nonabelian gauge theories which is capable of measuring a wider class of topological charges of monopole strings. The symmetry is invertible on compact spacetimes, but non-invertible on spacetimes with boundary. In the case of maximal supersymmetry, we show that this symmetry has a natural origin coming from the 6d $\mathcal N=(2,0)$ superconformal field theory under dimensional reduction. By generalizing this construction to any ADE gauge group, this allows us to propose a broad new class of homotopy invariants provided by the boundary non-invertible symmetry defects.