Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)
(Is this your paper?)
This 2011 paper by U.Harst and M. Reuter discusses the non-perturbative renormalization group flow of Quantum Electrodynamics (QED) coupled to Quantum Einstein Gravity (QEG) and explore the possibilities for defining its continuum limit at a fixed point that would lead to a non-trivial, i.e. interacting field theory.
''We find two fixed points suitable for the Asymptotic Safety construction. In the first case, the fine-structure constant vanishes at the fixed point and its infrared (renormalized) value is a free parameter not determined by the theory itself. In the second case, the fixed point value of the fine-structure constant is non-zero, and its infrared value is a computable prediction of the theory.''