Flat Self-dual Gravity

Understand

We construct a new covariant action for "flat" self-dual gravity in four spacetime 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.