  We study parity-violating effects, particularly the generation of angular
momentum density and its relation to the parity-odd and dissipationless
transport coefficient Hall viscosity, in strongly-coupled quantum fluid systems
in 2+1 dimensions using holographic method. We employ a class of
3+1-dimensional holographic models of Einstein-Maxwell system with gauge and
gravitational Chern-Simons terms coupled to a dynamical scalar field. The
scalar can condensate and break the parity spontaneously. We find that when the
scalar condensates, a non-vanishing angular momentum density and an associated
edge current are generated, and they receive contributions from both gauge and
gravitational Chern-Simons terms. The angular momentum density does not satisfy
a membrane paradigm form because the vector mode fluctuations from which it is
calculated are effectively massive. On the other hand, the emergence of Hall
viscosity is a consequence of the gravitational Chern-Simons term alone and it
has membrane paradigm form. We present both general analytic results and
numeric results which take back-reactions into account. The ratio between Hall
viscosity and angular momentum density resulting from the gravitational
Chern-Simons term has in general a deviation from the universal 1/2 value
obtained from field theory and condensed matter physics.
