Quantum Corrections to $η/s$ from JT Gravity

TL;DR

This work investigates how IR quantum fluctuations of near-extremal black branes, captured via Jackiw–Teitelboim (JT) gravity and its Schwarzian sector, modify the holographic shear viscosity to entropy ratio $\eta/s$ at finite chemical potential. By computing the quantum-corrected IR retarded Green's function and relating it to the UV function through the standard holographic dictionary, the authors introduce a temperature-dependent renormalized dimension $\ell'$ that encapsulates quantum effects and yields a corrected $\eta'/s'$ in two regimes: a semiclassical regime ($T\gg 1/C$) and a quantum regime ($T\ll 1/C$). They find that $\eta/s$ develops a nontrivial $T$-dependence, with a minimum below the KSS bound in the semiclassical region and a rapid rise above the bound in the deep quantum regime, driven by quantum corrections to the entropy $s'$, which includes a $\log(CT)$ term. The results are cross-checked against the quantum-corrected absorption cross-section, showing consistent transport-absorption behavior and offering insight into how finite-$N$ IR effects can alter hydrodynamic bounds in holographic theories.

Abstract

We revisit the computation of the shear viscosity to entropy ratio $η/s$ at finite chemical potential in a holographic model that takes into account the quantum fluctuations in the IR region of near-extremal black branes. Such quantum corrections can be computed from JT gravity and generate non-trivial temperature dependence for $η/s$, which deviates from the universal $1/4π$ result. In the semi-classical regime, $η/s$ attains a minimum which is below the KSS bound, generated by the presence of the quantum effects. In the quantum regime at lower temperatures, $η/s$ increases and is well above the KSS bound. We also compare the shear viscosity to the quantum-corrected absorption cross-section of near-extremal black holes, and find agreement.

Figures (2)

• Figure 4: The quantum-corrected shear viscosity-entropy ratio as a function of temperature in the semiclassical regime $CT\gg 1$. The dashed blue line denotes the KSS bound. We have chosen $\kappa = 1$, $L = 0.1$, $r_0 = 1$.
• Figure 5: The left panel shows the temperature dependence of the quantum-corrected shear viscosity-entropy ratio in the quantum regime $CT\ll 1$. The dashed blue line denotes the KSS bound and the dashed red line denoted the fitting function $4\pi(\eta'/s')=e^{-0.33}\times(CT)^{- 1.03}$. The right panel shows the same quantities in a log-log plot. The blue shaded area schematically represents the region where the entropy is negative, indicating the breakdown of the quantum-corrected $\eta/s$. We have set $\kappa = 1$, $L = 0.1$, $r_0 = 1$.