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

TL;DR

This paper explores the holographic duality between a $(2+1)$-dimensional parity-violating charged fluid and Chern-Simons modified gravity, revealing universal viscosity ratios and novel viscosity effects in both nondynamical and dynamical models.

Contribution

It introduces a detailed holographic description of parity-violating fluids in Chern-Simons gravity, including new viscosity coefficients and their dependence on cutoff surface and charge.

Findings

Shear viscosity to entropy density ratio $oxed{rac{ ext{eta}}{s} = rac{1}{4 ext{pi}}}$ is universal.

Hall viscosity to entropy density ratio depends on cutoff surface and charge.

Dynamical CS gravity introduces Curl viscosity with ratios depending on cutoff and charge.

Abstract

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 nonrelativistic long-wavelength expansion method, the field equations are solved up to $\mathcal{O}(\epsilon^2)$ 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 $\tilde{\partial}^2\beta_j=0$ 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 to $1/4\pi$ and the result of $\eta_A/s$ agrees to the previous result under the probe limit of the pseudo scalar field at the infinite boundary in the charged black brane background for the dynamical CS modified gravity. This vortical dual fluid corresponds to the magnetohydrodynamic (MHD) turbulence equation in plasma physics.