Abstract
We study renormalization group flow in a non-local version of quantum electrodynamics (QED). We determine the regime in which the theory flows to a local theory in the infrared and study a possible UV completion of four-dimensional QED. In addition, we find that there exist non-local conformal theories with a one-dimensional conformal manifold and non-local deformations of QED in three dimensions that are exactly marginal. Along the way we develop methods for coupling non-local derivatives to external sources and discuss unitarity and conformal vs. scale invariance of these theories.
Highlights
We study renormalization group flow in a non-local version of quantum electrodynamics (QED)
Treating the non-local kinetic term as the deformation of a local theory, we find that local three-dimensional QED possesses an exactly marginal non-local deformation Fμν D−1F μν
In this work we focused on non-local QED but many of the features studied here are robust and apply to a variety of other non-local theories
Summary
As mentioned in the introduction, and as we will discuss shortly, fields whose dynamics are controlled by non-local kinetic terms do not receive wavefunction renormalization. An alternate derivation of finiteness of the photon propagator for d = 3 and s = 1 can be found in [18, 20]. = 0 (so that the electric charge is not classically marginal) local kinetic terms may be generated during RG flow.
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