Discrete scale invariance in holography and an argument against the complexity=action proposal

The AdS/CFT correspondence often motivates research on questions in gravitational physics whose relevance might not be immediately clear from a purely GR-perspective, but which are nevertheless interesting. In these proceedings, we summarise two such results recently obtained by the author. One concerns, broadly speaking, the possible isometry-groups of a spacetime sourced by physical matter. The other one provides a possible argument against the recently proposed complexity=action conjecture.