Magnetic Soft Charges, Dual Supertranslations and 't Hooft Line Dressings

TL;DR

This paper constructs dual electric and magnetic soft dressings in quantum field theory, demonstrating electromagnetic duality and infrared finiteness, and extends the concept to gravitational dual supertranslations.

Contribution

It introduces magnetic 't Hooft line dressings as dual counterparts to electric Wilson lines, ensuring infrared finiteness and revealing duality in electric and magnetic soft modes.

Findings

Magnetic 't Hooft line dressings are charged under magnetic LGT.

Electric and magnetic soft modes exhibit electromagnetic duality.

Dual gravitational 't Hooft line dressings are constructed for asymptotically flat spacetime.

Abstract

We construct the Faddeev-Kulish asymptotic states in a quantum field theory of electric and magnetic charges. We find that there are two kind of dressings: apart from the well known (electric) Wilson line dressing, there is a magnetic counterpart which can be written as a 't Hooft line operator. The 't Hooft line dressings are charged under the magnetic large gauge transformation (LGT), but are neutral under electric LGT. This is in contrast to the Faddeev-Kulish dressings of electrons, which can be written as a Wilson line operator and are charged under electric LGT but neutral under magnetic LGT. With these dressings and the corresponding construction of the coherent states, the infrared finiteness of the theory of electric and magnetic charges is guaranteed. Even in the absence of magnetic monopoles, the electric and magnetic soft modes exhibit the electromagnetic duality of vacuum Maxwell theory. Using only the asymptotic form of three-point interactions in a field theory of electric and magnetic charges, we show that the leading magnetic dressings, like the leading electric ones, are exact in the field theory of electric and magnetic charges, in accordance with a conjecture of Strominger. We then extend the construction to perturbative quantum gravity in asymptotically flat spacetime, and construct gravitational 't Hooft line dressings that are charged under dual supertranslations. The duality in the quantum theory between the electric and magnetic soft charges and their dressings is thus made manifest.