Abstract
We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.
Highlights
Usefully characterised in terms of the scattering amplitudes that they produce
The main purpose of this paper is to describe a covariant action for SDGR that is applicable for metrics with zero scalar curvature
2.2 Relation to SDGR on anti-de Sitter space. There is another covariant action for SDGR [1], which is better suited for expansion over de Sitter space
Summary
The discussion of this section is phrased in terms of Euclidean signature gravity. anti-self-dual Einstein metrics are only non-trivial (i.e. not maximally symmetric) when the signature is Euclidean or split. One can interpret the constructions below as those for complexified GR
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