Holographic Complexity of Quantum Black Holes

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.

45 pages, 8 figures

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• Exploring Accelerating Hairy Black Holes in $2+1$ Dimensions: The Asymptotically Locally Anti-de Sitter Class and its Holography
• Angular momentum and chaos bound of charged particles around Einstein-Euler-Heisenberg AdS black holes
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• Entropy of Radiation with Dynamical Gravity
• Holographic complexity: braneworld gravity versus the Lloyd bound
• Perturbing a quantum black hole
• Mixed state information theoretic measures in boosted black brane
• Generalized holographic complexity of rotating black holes
• Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
• The Complexity of Being Entangled
• The Lamb shift in the BTZ spacetime
• Random Circuits in the Black Hole Interior
• Non-trivial saddles in microscopic description of black holes
• Complexity of Magnetization and Magnetic Simplification
• Entanglement Entropy and Complexity in Dyonic Quantum Black Holes
• Timelike entanglement and central charge for quantum BTZ black holes