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We use the holographic approach to compare the Hall viscosity $\eta_H$ andthe angular momentum density ${\cal J}$ in gapless systems in $2+1$ dimensionsat finite temperature. We start with a conformal fixed point and turn on aperturbation which breaks the parity and time reversal symmetries via gauge andgravitational Chern-Simons couplings in the bulk. While the ratio of $\eta_H$and ${\cal J}$ shows some universal properties when the perturbation isslightly relevant, we find that the two quantities behave differently ingeneral. In particular, $\eta_H$ depends only on infrared physics, while ${\calJ}$ receives contributions from degrees of freedom at all scales.

Hall Viscosity and Angular Momentum in Gapless Holographic Models