Abstract
In this paper based on the basic principles of gauge/gravity duality we compute the hall viscosity to entropy ratio in the presence of various higher derivative corrections to the dual gravitational description embedded in an asymptotically $ AdS_{4} $ space time. As the first step of our analysis, considering the back reaction we impose higher derivative corrections to the abelian gauge sector of the theory where we notice that the ratio indeed gets corrected at the leading order in the coupling. Considering the probe limit as a special case we compute this leading order correction over the fixed background of the charged black brane solution. Finally we consider higher derivative ($ R^{2} $) correction to the gravity sector of the theory where we notice that the above ratio might get corrected at the sixth derivative level.
Highlights
JHEP10(2014)015 corrections imposed solely on the gauge sector of the Einstein Maxwell gravity could affect the universality of the lower bound of the ηs/s ratio [42]–[43]
One of the well studied example of such a transport coefficient is the coefficient of hall viscosity that appears as the transport coefficient in the first order viscous hydrodynamics in (2 + 1) dimensions
The objective of the present analysis was to explore the hall viscosity to entropy ratio in presence of higher derivative corrections both on the gauge sector as well as on the gravity sector of the original theory proposed by Saremi and Son in [44]
Summary
Before we start our analysis it is always good to have a brief overview of the computations that we are going to do. In order to compute the response parameters associated with the first order viscous hydrodynamics at the boundary of the AdS4, we consider a derivative expansion of the velocity field (uμ), temperature (T ) as well as the charge (Q) in the bulk space time and solve the Einstein’s equation perturbatively upto leading order in that derivative expansion. The entire analysis is based on the two major facts, first one is that we shall lift the constant entities like T , Q and uμ to become slowly varying functions of the boundary coordinates (xμ) and the second one is that we shall carry out the analysis in a co-moving frame where the fluid two velocity is zero at the origin of the boundary coordinates namely xμ = 0 This enables us to write down the following expansion, ui = ui|x=0 + xμ∂μβi = xμ∂μβi.
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