How charge is renormalized by gravity

Electrical charge (the bare one), g, measures the coupling strength between electrons and photons. In QED, g is a constant. However, if interactions of QED fields with other fields (particles) are taken into account, the g shall be renormalized in the sense of renormalization group theory. In this article [doi:10.1038/nature09506], the author looks at how gravitational field renormalizes the g. In his treatment, there assumes a cutoff, below which the Einstein's theory is a reasonable starting point for quantization. Going through the usual RG procedures, he arrives at the statement that, gravity results in QED asymptotic freedom at high energy scales: g tends to zero at very large energy.

The first term on the right hand side of equation (12) is that present in the absence of gravity (found by letting kR0) and results in the electric charge increasing with energy. The second termis the correction due to quantum gravity. For pure gravity with L50, or for a small value of L as suggested by present observational evidence40, the quantum gravity contribution to the renormalization group b-function is negative and therefore tends to result in asymptotic freedom, in agreement with the
original calculation13.