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

Abstract

We discuss the (2 þ 1)-dimensional parity-violating charged fluid on a finite cutoff surface Σ c , dual to the nondynamical and dynamical Chern-Simons (CS) modified gravities. Using the nonrelativistic longwavelength expansion method, the field equations are solved up to Oðϵ 2 Þ in the nondynamical model. It is shown that there exists nonvortical dual fluid with shear viscosity η and Hall viscosity η A on the cutoff surface Σ c . The ratio of shear viscosity over entropy density η=s of the fluid takes the universal value 1=4π, while the ratio of Hall viscosity over entropy density η A =s depends on the Σ c and black brane charge q. Moreover, the nonvortical dual fluid obeys the magnetohydrodynamic (MHD) equation. However, these kinematic viscosities ν and ν A related to η and η A do not appear in this MHD equation due to the constraint condition∂ 2 β j ¼ 0 for the (2 þ 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 ζ A , whose ratio to entropy density ζ A =s also depends on the Σ c and q. Moreover, the value of η=s still equals 1=4π and the result of η 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.Since the pseudoscalar field is spacetime coordinate dependent, which leads to ∂ ν θ ≠ 0, then Eq. (5) reduces to DE-CHENG ZOU, YUNQI LIU, AND BIN WANG PHYSICAL REVIEW D 89, 064036 (2014) 064036-2

Hořava-Lifshitz gravity and effective theory of the fractional quantum Hall effect

“…This relation has been well established in the context of quantum Hall effects using other methods [29,30,47,49], but not confirmed from the Chern-Simons effective theory as far as we know, including in holography [139][140][141][142][143][144][145][146][147]. 4 We distinguish two types of angular momentum densities from the Chern-Simons effective theory and show that how the above relation arises (Section 5).…”

Membrane paradigm, gravitational Θ-term and gauge/gravity duality

“…19 Hall viscosity has been studied extensively in the context of Holography, e.g. see [58][59][60][61][62][63][64]69] where C mn is the Cotton-York tensor (4.15). Therefore, following [66], the Θ-term contribution to the energy-momentum tensor of the dual field theory is given by 20…”

Petrov type I condition and Rindler fluid in vacuum Einstein-Gauss-Bonnet gravity

“…where T (GB) ab is the one given in (6). Notice that P (α) ab in (35) has become the hypersurface function of extrinsic curvature K ab , but it is not true for δP (H) ab in (36). For example, we can see from [60] that the term…”

“…whereK ab is the contribution from vacuum Einstein gravity, and δK (α) ab includes the terms from the Gauss-Bonnet term at first order in small α expansion. Then from (35)…”

“…Significantly, the authors in [23] consider the fluid living on the finite cutoff hypersurface from the viewpoint of Wilsonian renormalization, there Dirichlet boundary condition on the hypersurface and the regularity on the horizon are imposed. Then the fluid/gravity correspondence on the cutoff hypersurface can be generalized to either asymptotically flat [24,25] or de Sitter spacetime [26], and it has been further studied in [27,28,29,30,31,32,33,34,35]. More general discussions in fluid/gravity correspondence can also be found in [36,37,38,39,40], as well as in the frame of AdS/Ricci-flat correspondence [41,42].…”