Reparameterization Dependence is Useful for Holographic Complexity

TL;DR

This paper explores how relaxing reparameterization invariance in holographic complexity calculations leads to finite, physically meaningful results, with vacuum AdS serving as a reference and black hole complexity saturating Lloyd's bound.

Contribution

It introduces a new approach to holographic complexity by relaxing reparameterization invariance, resulting in finite black hole complexity and clearer physical interpretation.

Findings

Black hole complexity becomes finite and saturates Lloyd's bound.

Vacuum AdS space is used as a reference state.

Artifacts like negative-time intervals are addressed.

Abstract

Holographic complexity in the "complexity equals action" approach is reconsidered relaxing the requirement of reparameterization invariance of the action with the prescription that the action vanish in any vacuum causal diamond. This implies that vacuum anti-de Sitter space plays the role of the reference state. Moreover, the complexity of an anti-de Sitter-Schwarzschild black hole becomes intrinsically finite and saturates Lloyd's bound after a critical time. It is also argued that several artifacts, such as the unphysical negative-time interval, can be removed by truly considering the bulk dual of the thermofield double state.