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.
Highlights
In this paper, we wish to point out that a defect conformal field theory which is free field theory in the bulk has some special properties which occur due to its geometry
We have examined the electromagnetic properties of a defect quantum field theory where the interacting charged particles reside on a 2+1-dimensional defect and the surrounding 3+1 dimensional bulk is occupied by a free photon field
We showed that the fully quantum corrected quantum theory remains a defect field theory in that the classical equations of motion for the electromagnetic fields which are induced by the presence of test charge and current densities are given by field equations where all of the interaction terms, including nonlinearities as well as corrections to the linear terms, are confined to the defect
Summary
We begin with the classical field, the one-point function of the photon, αμ(x), which is induced by the presence of the classical current jμ(x) in the partition function in equation (1.3), computed by. Xn), are (−1 times) the one-photon irreducible n-point defect current correlation functions, that is, the functions which appear in equation (2.5), but computed in the one-loop approximation. Since α is to be determined so that the one-point function of Aa(x) vanishes, the two-point function for Aa(x) which occurs in the second term on the right-hand-side of (2.12) must be connected It is the sum of terms, each term being the result of the removal of a different propagator, ∆ab(x, y), from Γint[α]. The full effective action necessarily has the form given in equation (2.4) which is a defect field theory. We will study the properties of the solution of the quantum corrected Maxwell’s equations in the weak field regime and in a few different scenarios
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