Holographic parity-violating charged fluid dual to Chern-Simons modified gravity

We discuss the (2 + 1)-dimensional parity-violating charged fluid on a finite cutoff surface Sigma(c), dual to the nondynamical and dynamical Chern-Simons (CS) modified gravities. Using the nonrelativistic long-wavelength expansion method, the field equations are solved up to O(epsilon(2)) in the nondynamical model. It is shown that there exists nonvortical dual fluid with shear viscosity eta and Hall viscosity eta(A) on the cutoff surface Sigma(c). The ratio of shear viscosity over entropy density eta/s of the fluid takes the universal value 1/4 pi, while the ratio of Hall viscosity over entropy density eta(A)/s depends on the Sigma(c) and black brane charge q. Moreover, the nonvortical dual fluid obeys the magnetohydrodynamic (MHD) equation. However, these kinematic viscosities nu and nu(A) related to eta and eta(A) do not appear in this MHD equation due to the constraint condition (partial derivative) over tilde (2)beta(j) = 0 for the (2 + 1)-dimensional dual fluid. Then, we extend our discussion to the dynamical CS modified gravity and show that the dual vortical fluid possesses another so-called Curl viscosity zeta(A), whose ratio to entropy density zeta(A)/s also depends on the Sigma(c) and q. Moreover, the value of eta/s still equals 1/4 pi and the result of eta(A)/s agrees with the previous result under the probe limit of the pseudoscalar field at the infinite boundary in the charged black brane background for the dynamical CS modified gravity. This vortical dual fluid corresponds to the MHD turbulence equation in plasma physics.