Abstract
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.
Highlights
Vortex flow [18,19,20]
We study parity-violating effects, 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 EinsteinMaxwell system with gauge and gravitational Chern-Simons terms coupled to a dynamical scalar field
Summary
The bulk action of our holographic Chern-Simons model in 3+1 dimension is:. where Fμν = ∂μAν − ∂νAμ is the field strength of Maxwell field. The bulk action of our holographic Chern-Simons model in 3+1 dimension is:. The cosmological constant Λ = −3/L2 and L is the AdS radius. Though in the actual calculation we will try to keep V [θ] general and not to implement this form until we have to. Θ[θ] is a general functional of θ. We will try to keep its form general for as long as possible in our calculation. Where nμ is the outgoing unit normal 1-form of the boundary and γμν = gμν − nμnν is the induced metric on the boundary. There is a Chern-Simons boundary term, analog to Gibbons-Hawking term, added such that the Dirichlet boundary value problem is well posed:
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