Holographic Complexity of Quantum Black Holes

TL;DR

This paper compares different holographic complexity proposals for quantum black holes, specifically the quantum BTZ black hole, revealing that Volume Complexity aligns well with quantum corrections while Action Complexity faces issues due to singularity contributions.

Contribution

It provides a detailed analysis of holographic complexity in quantum black holes, demonstrating the consistency of Volume Complexity and the challenges with Action Complexity in quantum regimes.

Findings

Volume Complexity admits a consistent quantum expansion

Action Complexity receives large contributions from the singularity

Quantum fields' complexity vanishes at leading order in holographic induced gravity

Abstract

We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields with large central charge in the presence of the black hole, including the backreaction corrections to the BTZ metric. Our results show that Volume Complexity admits a consistent quantum expansion and correctly reproduces known limits. On the other hand, the generalized Action Complexity picks up large contributions from the singularity, which is modified due to quantum backreaction, with the result that Action Complexity does not reproduce the expected classical limit. Furthermore, we show that the doubly-holographic setup allows computing the complexity coming purely from quantum fields - a notion that has proven evasive in usual holographic setups. We find that in holographic induced-gravity scenarios the complexity of quantum fields in a black hole background vanishes to leading order in the gravitational strength of CFT effects.