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 field in terms of a dual two-form gauge field. 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 field.The dual picture introduces two new puzzles: the charges have very unexpected Poisson brackets with the fields, and the monopole term does not 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 free scalar theory has new edge modes at infinity that canonically commute with all the bulk degrees of freedom.

Electromagnetic and color memory in even dimensions

“…The observed difference between radial and Lorenz gauge is one concrete facet of a general issue concerning the possible gauge-dependence of the asymptotic analysis [35,[41][42][43]. While in some instances, such as the present one, this problem has been clarified, the general systematics may still deserve further attention.…”

Asymptotic renormalization in flat space: symplectic potential and charges of electromagnetism

“…surfaces is the integral of the (antisymmetrized) variation of its normal component. 8 Since N a is the inward facing normal, the integration comes with a sign. Hence, the contribution to the symplectic form from an interval I(Ω) is…”

“…Firstly, adding a boundary term to the action adds a total variation to the SP (which does not change the symplectic form). Secondly, sinceθ a is defined only implicitly through (8), it is ambiguous by the divergence of an antisymmetric tensor. The ambiguities arê…”

“…Splitting the divergence in the defining relation (8) for the SP, δL =Ê a δA a +∂ aθ a , into a divergence on the Ω = const. surfaces and a transverse derivative by using the decomposition (4) of the identity, one obtains…”

“…The situation is enriched by the fact that dual charges have been recently suggested to also play a crucial role, once again both at asymptotic[6][7][8] and finite boundaries[9,10], as well as in gravity[11].…”