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

TL;DR

This paper discusses the isometry groups of matter-sourced spacetimes in holography and presents an argument challenging the validity of the complexity=action conjecture in the context of AdS/CFT.

Contribution

It offers new insights into spacetime symmetries in holography and critically examines the complexity=action proposal, questioning its applicability.

Findings

Identifies constraints on isometry groups of matter-influenced spacetimes

Provides a theoretical argument against the complexity=action conjecture

Highlights implications for holographic complexity studies

Abstract

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.