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.
Highlights
The electromagnetic duality of the vacuum Maxwell theory is broken in quantum electrodynamics with only electric sources
Having obtained the asymptotic states, we show that the soft photon dressing associated to these states can be written as a ’t Hooft line operator along the asymptotic trajectory of the magnetically charged particle
We study the algebra of dual supertranslation charges and the ’t Hooft line dressings for smooth parameter functions on the sphere
Summary
The electromagnetic duality of the vacuum Maxwell theory is broken in quantum electrodynamics with only electric sources. The Faddeev-Kulish dressings can be understood as operators that carry a definite charge of the asymptotic symmetry [13,14,21,22] This line of investigation has been applied, as mentioned above, to theories with electric and magnetic charged particles (and dyons) [2]. We emphasize that the field theory formulation of [24,25,26] is used only in the spirit of an effective field theory to determine the structure of the asymptotic three-point interaction This construction at large times is nonperturbative, since the states can be derived by other nonperturbative methods, such as writing Wilson line dressings or building eigenstates of the soft charge associated with the asymptotic symmetry.
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