I wrote previously about this approach to quantum gravity and in some sense it is a reason this blog still exists.
Recently, Frank Saueressig et al. were able to answer an important question and argue that their "result vanquishes the longstanding criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projection space."
There were some comments about it on Jacques Distler's blog, who posted about a different paper.
Let me admit that I understand less than half of what he wrote about soft gravitons and photons, but it does seem to me now that asymptotic safety is in better shape than he thought previously.
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