Schwarzian quantum corrections to shear correlators of the near-extremal Reissner-Nordström-AdS black hole

TL;DR

This work analyzes how bulk quantum fluctuations governed by the Schwarzian effective theory modify the low-temperature shear dynamics of near-extremal RN–AdS4 black holes with flat horizons. Using exact Schwarzian correlators and a careful inner/outer matching in the RN–AdS4 geometry, it derives a quantum-corrected IR Green's function with Δ=0, yielding a corrected shear conductivity and diffusivity that modestly raise η and D_⊥ in the hydrodynamic regime while preserving the Kovtun-Son-Starinets bound. The results show that Schwarzian fluctuations lift the classically gapless T=0 shear mode outside the hydrodynamic regime, and provide a controlled framework to study how bulk quantum effects feed into boundary transport. The analysis also clarifies the importance of boundary conditions for the IR operator and outlines clear directions for extending the approach to other sectors and higher-dimensional black holes, with potential implications for holographic analogs of fluctuating hydrodynamics. Overall, the paper demonstrates that Schwarzian quantum corrections can quantitatively affect transport properties in near-extremal holographic systems without violating fundamental bounds at the order considered.

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-Nordström-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 $s/(4π)$, thereby preserving the Kovtun-Son-Starinets bound. Outside the hydrodynamic regime, quantum fluctuations lift the zero temperature, classical gapless modes reported in previous literature.

Figures (4)

• Figure 1: By performing a Wick rotation with Euclidean time $\tau^\text{E}_{12}\gtrless 0$ in Eq. \ref{['eq:vev_2pt']}, one obtains respectively the Wightman correlators $G^{\pm}_\Delta$.
• Figure 2: Complex $z$ plane for $\log(z)$ to evaluate the difference in Eq. \ref{['eq:Delta_log']}.
• Figure 3: The Wick rotation is performed by first analytically continuing the Euclidean correlator onto the strip $\mathbb{R}\times(\frac{\beta-\beta_\text{eff}}{2},\frac{\beta+\beta_\text{eff}}{2})$ and then extending beyond the branch cut to access the $0^+$ prescription lines. The correlator being periodic in $\beta$, the line $\tau_\text{E}=0$ and $\tau_\text{E}=\beta$ are identified, implying a discontinuity there.
• Figure 4: Evaluating the $\log(z)$ difference in \ref{['eq:I2p-I2m']} in the complex $z$ plane.