Flat Self-dual Gravity

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.

18 pages

References in corpus (6)

• The Kinematic Algebra From the Self-Dual Sector
• Light-Front Higher-Spin Theories in Flat Space
• Actions for Self-dual Higher Spin Gravities
• A double copy for asymptotic symmetries in the self-dual sector
• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• Chiral perturbation theory for GR

Cited by in corpus (14)

• Actions for Self-dual Higher Spin Gravities
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• Toward a twistor action for chiral higher-spin gravity
• Minimal models of field theories: Chiral Higher Spin Gravity
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Quantizing the non-linear graviton
• Minimal model of Chiral Higher Spin Gravity
• Towards higher-spin holography in flat space
• Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions
• Minimal models of field theories: SDYM and SDGR
• One-loop same helicity YM amplitudes from BG currents
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• Massless chiral fields in six dimensions
• Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes