Effective field theory of quantum gravity coupled to scalar electrodynamics

TL;DR

This paper uses effective field theory to analyze how quantum gravity coupled to scalar electrodynamics affects the renormalization of gauge couplings, finding gravitational effects do not modify charge running.

Contribution

It demonstrates that gravitational interactions do not influence the beta function of the electric charge in scalar electrodynamics within an effective field theory framework.

Findings

Gravitational corrections do not alter the gauge coupling beta function.

The model is renormalizable up to dimension six operators.

Quantum gravity effects are negligible on charge running at low energies.

Abstract

In this work we use the framework of effective field theory to couple Einstein's gravity to scalar electrodynamics and determine the renormalization of the model through the study of physical processes below Planck scale, a realm where quantum mechanics and general relativity are perfectly compatible. We consider the effective field theory up to dimension six operators, corresponding to processes involving one graviton exchange. Studying the renormalization group functions we see that the beta function of the electric charge is positive and possesses no contribution coming from gravitational interaction. Our result indicates that gravitational corrections do not alter the running behavior of the gauge coupling constants, even if massive particles are present.