QED coupled to QEG
  We discuss 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. 
Ulrich Harst and Martin Reuter
hep-th