Hall Viscosity and Angular Momentum in Gapless Holographic Models

Understand

We use the holographic approach to compare the Hall viscosity $\eta_H$ 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 $\eta_H$ 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, $\eta_H$ depends only on infrared physics, while ${\cal J}$ receives contributions from degrees of freedom at all scales.