Scalar Asymptotic Charges and Dual Large Gauge Transformations

TL;DR

This paper reveals that scalar soft theorems correspond to asymptotic charges generated by large gauge transformations of a dual two-form field, extending the gauge symmetry framework to scalar theories and uncovering new edge modes at infinity.

Contribution

It introduces a dual two-form gauge field approach to interpret scalar soft theorems as large gauge symmetries, filling a gap in the symmetry understanding of scalar theories.

Findings

Scalar soft theorems are linked to large gauge transformations of dual fields.

The dual picture reveals unexpected Poisson brackets and edge modes at infinity.

Analogies with Kramers-Wannier duality suggest new boundary degrees of freedom.

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.