Defect QED: Dielectric without a Dielectric, Monopole without a Monopole

TL;DR

This paper explores a defect quantum field theory where a 2+1D defect influences 3+1D bulk electromagnetism, resulting in dielectric-like behavior and novel electromagnetic phenomena, especially in quantum Hall and graphene systems.

Contribution

It demonstrates that defect quantum field theories can exhibit dielectric-like electromagnetic properties and introduces new effects such as image dyons in time-reversal violating states.

Findings

Electromagnetic fields are attenuated as if in a dielectric medium.

Image charges can appear as dyons in time-reversal violating states.

Charge screening effects are significant in graphene and metallic layers.

Abstract

We study a class of defect quantum field theories where the quantum field theory in the 3+1-dimensional bulk is a free photon and charged matter and the interactions of the photons with the charges occur entirely on a 2+1-dimensional defect. We observe that at the fully quantum level, the effective action of such a theory is still a defect field theory with free photons propagating in the bulk and the nonlinearities in the quantum corrections to the Maxwell equations confined to the defect. We use this observation to show that the defect field theory has interesting electromagnetic properties. The electromagnetic fields sourced by static test charges are attenuated as if the bulk surrounding them were filled with a dielectric material. This is particularly interesting when the observer and test charge are on opposite sides of the defect. Then the effect is isotropic and it is operative even in the region near the defect. If the defect is in a time reversal violating state, image charges have the appearance of electrically and magnetically charged dyons. We present the example of a single layer in a quantum Hall state. We observe that the charge screening effect in charge neutral graphene should be significant, and even more dramatic when the layer is in a metallic state with mobile electrons.