## Holographic parity violating charged fluid dual to Chern-Simons modified gravity    [PDF]

De-Cheng Zou, Bin Wang
We discuss the $(2+1)$-dimensional parity violating charged fluid with Hall viscosity $\eta_A$ and Curl viscosity $\zeta_A$ on a finite cutoff surface $\Sigma_c$, dual to the dynamical Chern-Simons (CS) modified gravity. Using nonrelativistic long-wavelength expansion, we find that the dual fluid obeys incompressible charged Navier-Stokes equation with external force density influenced by the pseudo scalar and electromagnetic fields. On the $\Sigma_c$, the ratio of shear viscosity over entropy density $\eta/s$ of the fluid is independent of the cutoff surface and does not receive any influence from the gravitational and electromagnetic CS terms. While the ratio of Hall viscosity over entropy density $\eta_A/s$ depends on the cutoff surface and black brane charge. Our result agrees to the previous result under the probe limit of the pseudo scalar field at the infinite boundary in the charged black brane background. We find that holographic fluid/gravity duality cannot be realized in the non-dynamical CS gravity in the black brane background. It can only be set up in the dynamical CS gravity.
View original: http://arxiv.org/abs/1306.5486