Quantum gravity, gauge coupling constants, and the cosmological constant

TL;DR

This paper investigates how quantum gravity with a cosmological constant affects gauge coupling constants, revealing gauge condition dependence and proposing the Vilkovisky-DeWitt method to obtain gauge-invariant results, with implications for high-energy physics.

Contribution

It introduces a gauge-invariant approach to quantize Einstein-Maxwell theory with a cosmological constant, analyzing its impact on gauge coupling renormalization.

Findings

Quantum gravity with a cosmological constant influences the running of gauge couplings.

Traditional background-field methods show gauge condition dependence.

Vilkovisky-DeWitt method yields gauge-invariant results and suggests an ultraviolet fixed point.

Abstract

The quantization of Einstein-Maxwell theory with a cosmological constant is considered. We obtain all logarithmically divergent terms in the one-loop effective action that involve only the background electromagnetic field. This includes Lee-Wick type terms, as well as those responsible for the renormalization group behaviour of the electric charge (or fine structure constant). Of particular interest is the possible gauge condition dependence of the results, and we study this in some detail. We show that the traditional background-field method, that is equivalent to a more traditional Feynman diagram calculation, does result in gauge condition dependent results in general. One resolution of this is to use the Vilkovisky-DeWitt effective action method, and this is presented here. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This re-opens the possibility, suggested by Robinson and Wilczek, of altering the scaling behaviour of gauge theories at high energies although our result differs. We show the possibility of an ultraviolet fixed point that is linked directly to the cosmological constant.