Many quantum-gravity theories are strongly interacting. It is not clear if they produce the gravity as we know it at low energies. So I wonder, is there any quantum-gravity theory that
a) is a well defined quantum theory at non-perturbative level (ie can be put in a computer to simulate it, at least in principle).
b) produces nearly flat space-time.
c) contains gravitons as the ONLY low energy excitations. (ie the helicity $\pm 2$ modes are the ONLY low energy excitations.)
We may replace c) by
c') contains gravitons and photons as the ONLY low energy excitations. (ie the helicity $\pm 2$ and $\pm 1$ modes are the ONLY low energy excitations. This is the situation in our universe.)