Asymptotic structure of scalar-Maxwell theory at the null boundary

We apply the Hamiltonian formalism to investigate the massless sector of scalar field theory coupled with Maxwell electrodynamics through the Pontryagin term. To this end, we generalize the Dirac procedure to include radially independent zero modes of the symplectic matrix associated with the asymptotic symmetries. Specifically, we analyze asymptotic symmetries at the null infinity of this theory, conserved charges, and their algebra. We find that the theory possesses asymptotic shift symmetries of the fields not present in the bulk manifold coming from the zero modes of the symplectic matrix of constraints. Consequently, we conclude that the real scalar field also contains asymptotic symmetries previously found in the literature by a different approach. We show that these symmetries can be seen as the electric-magnetic duality in electromagnetism with the topological Pontryagin term, and obtain a nontrivial central extension between the electric and magnetic conserved charges. Finally, we examine the full interacting theory and find that, due to the interaction, the symmetry generators are more difficult to identify among the constraints, such that we obtain them in the weak-coupling limit. We find that the asymptotic structure of the theory simplifies due to a fast fall-off of the scalar field, leading to decoupled scalar and Maxwell asymptotic sectors, and losing the electric-magnetic duality.