Hall Viscosity and Angular Momentum in Gapless Holographic Models

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

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