Orateur
Description
Extremal black holes have the particularity to exhibit an emergent geometry close to their horizon that contains an AdS2 factor. For compact internal spaces, the theory can be dimensionally reduced to obtain a dilaton gravity in two dimensions. At the linearised level, this reduces to JT gravity. The low-energy effective theory is governed by the Schwarzian action, enabling corrections to the entropy and to correlators of the dual near CFT1 to be computed, arising from quantum fluctuations of near-horizon zero modes. By studying shear diffusion, it is in principle possible to compute the effect of these corrections on the ratio viscosity over entropy density, which is conjectured to have a positive lower bound for any fluid. Saturated in numerous holographic systems at the classical gravity level, we address whether such quantum corrections change the picture. Using a matching calculation, we focus on the hydrodynamic regime, for which only weak quantum fluctuations can be considered in order to avoid entering a sub-Planckian regime. We find that the results obtained from the transverse Kubo formula and the one from the location of the diffusive pole in the shear sector agree.
