Flat Self-dual Gravity

TL;DR

This paper introduces a new covariant action for flat self-dual gravity in four dimensions, capturing its dynamics with a single-term formulation that aligns with known gauge theories and exhibits double copy structure.

Contribution

It presents the first covariant, single-term action for flat self-dual gravity, paralleling self-dual Yang-Mills theory and revealing double copy properties.

Findings

Action reproduces chiral interactions in light-cone gauge

Single-term action simplifies understanding of self-dual gravity

Demonstrates double copy structure with self-dual Yang-Mills

Abstract

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. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.