Low-temperature Quantum-corrected Holographic Transport with Momentum Relaxation

We determine the quantum corrections to transport arising from fluctuations of the near-AdS${}_2$ throat of near-extremal black branes in holographic models with momentum relaxation. By computing the shear viscosity and electrical conductivity at both zero and finite chemical potential, we uncover a universal low-temperature enhancement of transport generated by Schwarzian quantum fluctuations. Specifically, transport coefficients extracted from retarded Green's functions increase throughout the regime $C T \ll 1$. For operators with Schwarzian scaling dimension $\Delta >1$, this enhancement is preceded by a universal minimum at a characteristic temperature $T_{\rm min} \propto C^{-1}$, leading to a non-monotonic temperature dependence strikingly similar to that observed in many correlated materials. In contrast, for the case $\Delta =1$, relevant for the electrical conductivity, the transport coefficient evolves monotonically toward a constant value. Our results identify universal signatures of near-horizon quantum gravity in the transport properties of holographic quantum matter.