this paper came out today https://arxiv.org/abs/1610.01457 Self-Dual Gravity Kirill Krasnov (Submitted on 5 Oct 2016) Self-dual gravity is a diffeomorphism invariant theory in four dimensions that describes two propagating polarisations of the graviton and has a negative mass dimension coupling constant. Nevertheless, this theory is not only renormalisable but quantum finite, as we explain. We also collect various facts about self-dual gravity that are scattered across the literature. there is also an extensive literature on self-dual loop quantum gravity, when y=i the paper states self-dual gravity, but makes no mention of self-dual loop quantum gravity, claims self-dual gravity is analogous to self-dual yang mills, and is finite as is the only native 4-d gravity whose quantum version in pure gravity that is finite says string theory could be finite in 4d with compactification but also predicts infinite number of fields. self-dual also has connections with penrose twistor theory. what is current evaluation of self dual gravity and why does it get so little mention? krasnov claims it is finite quantum version in 4 d. what is current evaluation of self-dual yang mills and can the SM be rewritten in a self-dual yang mills theory?