TL;DR
Self-dual gravity is a four-dimensional, diffeomorphism-invariant theory that describes two graviton polarizations, is renormalisable and finite at the quantum level, and has a negative mass dimension coupling constant.
Contribution
The paper consolidates scattered knowledge about self-dual gravity and explains its renormalisability and quantum finiteness despite having a negative mass dimension coupling.
Findings
Self-dual gravity describes two graviton polarizations.
The theory is renormalisable and quantum finite.
It has a negative mass dimension coupling constant.
Abstract
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.
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