Schwarzian quantum corrections to shear correlators of the near-extremal Reissner-Nordstr\"om-AdS black hole

TL;DR

This paper investigates how quantum fluctuations, modeled by the Schwarzian theory, affect shear correlators in near-extremal Reissner-Nordström-AdS black holes, revealing increased shear viscosity and lifted zero-temperature modes.

Contribution

It provides exact quantum-corrected scalar correlation functions in Schwarzian theory and applies them to analyze shear correlators in near-extremal black holes.

Findings

Quantum fluctuations increase shear viscosity, maintaining the KSS bound.

Quantum effects lift zero-temperature gapless modes.

Schwarzian corrections resolve thermodynamic puzzles in near-extremal black holes.

Abstract

Near-AdS$_2$ spacetimes are controlled by a Schwarzian effective dual theory. The Kaluza-Klein reduction of higher-dimensional black holes shows that the Schwarzian generates a logarithmic contribution to the entropy, thereby resolving a long-standing puzzle in near-extremal black hole thermodynamics. Here, we leverage exact results for quantum-corrected, Schwarzian scalar correlation functions in order to evaluate the impact of bulk quantum fluctuations on the low-temperature shear correlators of the state dual to Reissner-Nordstr\"om-AdS$_4$ black holes with a flat, compact horizon. In the hydrodynamic regime, we find that quantum fluctuations tend to increase the shear viscosity away from $s/(4\pi)$, thereby preserving the Kovtun-Son-Starinets bound. Outside the hydrodynamic regime, quantum fluctuations lift the zero temperature, classical gapless modes reported in previous literature.