Hall Viscosity and Angular Momentum in Gapless Holographic Models

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We use the holographic approach to compare the Hall viscosity ηₕ and the angular momentum density 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 ηₕ and J shows some universal properties when the perturbation is slightly relevant, we find that the two quantities behave differently in general. In particular, ηₕ depends only on infrared physics, while J receives contributions from degrees of freedom at all scales.