Quantum Corrections to $\eta/s$ from JT Gravity

Abstract

We revisit the computation of the shear viscosity to entropy ratio $\eta/s$ 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 $\eta/s$, which deviates from the universal $1/4\pi$ result. In the semi-classical regime, $\eta/s$ attains a minimum which is below the KSS bound, generated by the presence of the quantum effects. In the quantum regime at lower temperatures, $\eta/s$ 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.