Finite quantum gauge theories

TL;DR

This paper develops a nonlocal extension of gauge theories like Yang-Mills and QED, achieving one-loop exact beta functions, UV finiteness, and solving Landau pole issues through specific potential terms.

Contribution

It introduces a weakly nonlocal gauge theory with a potential that renders the beta function zero, leading to a UV finite and ghost-free model.

Findings

The theory is perturbatively super-renormalizable and unitary.

The potential can be chosen to make the beta function vanish.

The dressed propagator avoids Landau poles in UV and IR.

Abstract

We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of running gauge coupling constant. The outcome is "a UV finite theory for any gauge interaction". Our calculations are done in D=4, but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite we are able to solve also the Landau pole problems, in particular in QED. Without any potential the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV, nor the singularities in the infrared regime (IR).