Electric-magnetic duality in linearized Ho\v{r}ava-Lifshitz gravity

Understand

Known as a symmetry of vacuum Maxwell equations, the electric-magnetic duality can be lifted actually to a symmetry of an action.

• The Lagrangian of this action is written in terms of two vector potentials, one electric and one magnetic, and while it is manifestly invariant under duality rotations, it is not manifestly Lorentz covariant.
• This duality symmetry exists also in linearized gravity in four dimensions, and can be lifted off shell too.
• In $d$ dimensions, the link between linearized gravity and its dual can also be seen from the point of view of a parental action.