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.

Bath deformations, islands and holographic complexity

“…See[71,[91][92][93][94][95][96][97][98][99][100][101][102][103] for various computations of holographic and subregion complexity.…”

Quantum Extremal Islands Made Easy, Part IV: Massive Black Holes on the Brane

“…With hindsight, we can see that this arises because the brane becomes a nontrivial source for the gravitational field in higher dimensions, and deforms the background by backreacting to the geometry in a non-trivial way. An interesting step towards such higher dimensional investigation comes with the d = 3 construction recently examined in [112,113].…”

“…For example, examining how the phase transition is modified in the case of higher dimensions. Again, the recent d = 3 construction [112,113] is a natural framework to investigate this question. Another question would be to investigate the effect moving the position of the second defect away from φ = π.…”

“…Other interesting directions would be to study holographic complexity in our framework, following the approach discussed in [3] -see also [46,113,114]. Finally, let us comment that since the horizon has a finite size in our construction, it is amenable to a fuzzball description, e.g., [115,116].…”

Mixed state information theoretic measures in boosted black brane

“…Some interesting works related to the holographic computation of complexity can be found in [70][71][72][73][74][75][76][77][78][79][80]. Now in this set up (where the subsystem is taken to be along the direction of the boost), if V (γ) denotes the maximal co-dimension-one volume enclosed by the co-dimension-two static, minimal Ryu-Takayanagi (RT) surface in the bulk, then the holographic subregion complexity (HSC) reads…”