Scalar Asymptotic Charges from Dual Large Gauge Transformations

We show that, in four dimensions, almost all the soft charges that canonically generate the scalar soft theorem are large gauge ransformations of a dual two-form gauge field. The dual picture also resolves an apparent paradox where the charges were not symmetries of the scalar field theory. However, the dual picture introduces two new puzzles: it turns out that the soft charges have very unexpected Possion brackets with the fields, and that the soft charge that is constant on the sphere, and only that one, doesn’t always have a dual gauge transformation interpretation. We find analogs of these two properties in the Kramers-Wannier duality on a finite lattice, indicating that the scalar theory has new edge modes at infinity that canonically commutes with all the bulk degrees of freedom.(Work in progress with Miguel Campiglia, Florian Hopfmueller and Laurent Freidel.)