Universality of gauge coupling constant in the Einstein-QED system

TL;DR

This paper investigates how the gauge coupling constant in Einstein-QED remains universal under renormalization, showing that Ward identities ensure its invariance despite gravitational contributions at one-loop order.

Contribution

It demonstrates the preservation of gauge coupling universality in Einstein-QED within an effective field theory framework, emphasizing the role of Ward identities.

Findings

Renormalization of three-point functions varies with particle type.

Ward identities protect gauge coupling universality at one-loop.

Gravitational sector does not alter electric charge renormalization at one-loop.

Abstract

In this paper we discuss the universality of the renormalization of the gauge coupling constant in the quantum electrodynamics coupled to the Einstein's gravity in the framework of effective field theory in an arbitrary gauge. We observe that the renormalization of the three-point functions with different particles receive different contributions from the gravitational sector. Despite that, the universality of the gauge coupling constants is guaranteed by the Ward identity that makes the renormalized electric charge receive no contribution from the gravitational sector at one-loop order.