Holographic Complexity Of Cold Hyperbolic Black Holes

TL;DR

This paper investigates the holographic complexity of hyperbolic black holes in AdS, revealing a logarithmic scaling with temperature and suggesting possible generalizations to other near-extremal systems with conformal quantum mechanics.

Contribution

It demonstrates that hyperbolic black holes exhibit an anomalously large holographic complexity that scales logarithmically with temperature, a novel insight into their low-temperature behavior.

Findings

Complexity scales logarithmically with temperature.

Hyperbolic black holes have a large ground state degeneracy.

Potential generalization to other near-extremal systems.

Abstract

AdS black holes with hyperbolic horizons provide strong-coupling descriptions of thermal CFT states on hyperboloids. The low-temperature limit of these systems is peculiar. In this note we show that, in addition to a large ground state degeneracy, these states also have an anomalously large holographic complexity, scaling logarithmically with the temperature. We speculate on whether this fact generalizes to other systems whose extreme infrared regime is formally controlled by Conformal Quantum Mechanics, such as various instances of near-extremal charged black holes.