One-loop Corrected Holographic Shear Viscosity to Entropy Density Ratio at Low Temperatures

Near-extremal black holes are known to contain strong quantum fluctuations in their near-horizon near-AdS$_2$ throat region governed by an effective action that includes Schwarzian modes. These fluctuations lead to one-loop corrections in the gravitational path integral that are essential in understanding the thermodynamics of near-extremal black holes at low temperatures where they become more dominant that the semi-classical answer. We explore the implications of these quantum fluctuations for near-extremal asymptotically AdS$_4$ black branes in the context of the AdS/CFT correspondence. We note that at one-loop level there is a coupling of the shear gravitational fluctuations to one of the would-be zero modes. This coupling affects the retarded Green's function in a way that leads to a low temperature violation of the shear viscosity to entropy density bound.