Scalar asymptotic charges and dual large gauge transformations

Abstract

In recent years soft factorization theorems in scattering amplitudes have been reinterpreted as conservation laws of asymptotic charges. In gauge, gravity, and higher spin theories the asymptotic charges can be understood as canonical generators of large gauge symmetries. Such a symmetry interpretation has been so far missing for scalar soft theorems. We remedy this situation by treating the massless scalar eld in terms of a dual twoform gauge eld. We show that the asymptotic charges associated to the scalar soft theorem can be understood as generators of large gauge transformations of the dual two-form eld. The dual picture introduces two new puzzles: the charges have very unexpected Poisson brackets with the elds, and the monopole term does not always have a dual gauge transformation interpretation. We nd analogues of these two properties in the Kramers-Wannier duality on a nite lattice, indicating that the free scalar theory has new edge modes at in nity that canonically commute with all the bulk degrees of freedom.