Quantum-gravity predictions for the fine-structure constant

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.