Quantum-gravity predictions for the fine-structure constant

TL;DR

This paper explores how asymptotically safe quantum gravity can determine the value of the electromagnetic fine-structure constant by analyzing the fixed points of gauge coupling running influenced by gravity and matter fluctuations.

Contribution

It introduces a framework where quantum gravity effects fix the gauge coupling, enabling a calculable prediction of the fine-structure constant based on matter content.

Findings

Predicts a specific value of the fine-structure constant at the Planck scale.

Shows the fixed point behavior of gauge coupling influenced by gravity and matter fluctuations.

Highlights the dependence of the prediction on matter content and computational uncertainties.

Abstract

Asymptotically safe quantum fluctuations of gravity can uniquely determine the value of the gauge coupling for a large class of grand unified models. In turn, this makes the electromagnetic fine-structure constant calculable. The balance of gravity and matter fluctuations results in a fixed point for the running of the gauge coupling. It is approached as the momentum scale is lowered in the transplanckian regime, leading to a uniquely predicted value of the gauge coupling at the Planck scale. The precise value of the predicted fine-structure constant depends on the matter content of the grand unified model. It is proportional to the gravitational fluctuation effects for which computational uncertainties remain to be settled.