Quantum Corrections in the Low-Temperature Fluid/Gravity Correspondence

TL;DR

This work analyzes the breakdown of hydrodynamics at very low temperatures in the fluid/gravity correspondence by pinpointing logarithmic infrared contributions tied to the AdS$_2$ throat. It introduces quantum corrections inspired by Jackiw-Teitelboim gravity and the Schwarzian action, yielding a new scale $C$ that governs symmetry breaking and stabilizes the long-wavelength fluid dynamics through Schwarzian averaging. The authors derive quantum-corrected thermodynamics, linear-response constitutive relations, and dispersion relations for all hydrodynamic modes in near-extremal RN-AdS$_4$, finding that $\eta/s$ can be violated from the universal bound at sufficiently low $T$. This framework clarifies the role of IR modes in holographic fluids and offers a controlled way to incorporate quantum fluctuations into low-temperature fluid dynamics with potential implications for strongly coupled quantum systems and quantum black hole physics.

Abstract

Attempts to construct a low-temperature version of the fluid/gravity correspondence have faced obstacles manifested in the form of logarithmic terms in the frequency, $\log(ω)$, leading to non-local in time constitutive relations for the stress tensor and the charge current. These difficulties can be broadly presented as a breakdown of the hydrodynamic description due to additional infrared modes. We employ new quantum insights into the physics of near-extremal black holes, brought about in the context of Jackiw-Teitelboim gravity, as an effective description of quantum fluctuations in the throat, to revisit the fluid/gravity correspondence at very low temperatures. The quantum corrections naturally include a new length scale, $C$, and an effective action that parametrizes the breaking of near-horizon symmetries. We show that with an appropriate choice of order of limits in the derivative expansion within the low-temperature regime, the $\log(ω)$ infrared divergence can be resolved. By quantum averaging the infrared Schwarzian modes as an effective extra contribution to the long-wavelength fluid modes, the resulting low-temperature effective fluid description is consistent. We present the dispersion relations for all the relevant hydrodynamic modes. We also revisit the shear viscosity to entropy density ratio and find that at very low temperatures the universal $\frac{1}{4π}$ bound is violated due to quantum correction.

Figures (7)

• Figure 1: Regime Choice and Local-Equilibrium
• Figure 2: Temperature dependence of $\eta$ at $C=1,\,r_h=100$. The red line represents the quantum-corrected $\eta$ in the $T<T_q$ limit, and the blue line represents the semi-classical area law of $\eta$.
• Figure 3: Temperature dependence of $\eta/s$ with $C=1\,,r_h=100$.
• Figure 4: Temperature dependence of $\eta/s$ in fixed $C=1$ and different $\mu$.
• Figure 5: Temperature dependence of $\chi_1$ and $\chi_2$ at $r_h=100$, where the left figure is $\chi_{1}/(\frac{r_h}{4\pi G})$ and the right figure is $\chi_2/(\frac{1}{4\pi G})$.