Holographic complexity of quantum black holes

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.

Automated summary

This study analyzes different holographic complexity proposals for black holes, considering corrections from bulk quantum fields. By focusing on the quantum BTZ black hole, the analysis accounts for the effects of conformal fields with large central charge and backreaction corrections to the BTZ metric. The results indicate that Volume Complexity exhibits a consistent quantum expansion and accurately reproduces known limits, while the Generalized Action Complexity fails to reproduce the expected classical limit due to large contributions from the singularity modified by quantum backreaction. Moreover, the doubly-holographic setup enables the computation of complexity purely from quantum fields, a concept that has been challenging in conventional holographic setups. 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.