Magnetotransport from the fluid/gravity correspondence
Journal of High Energy Physics
We continue our construction of a hydrodynamical description of a holographic model with broken translation invariance. Using the fluid/gravity correspondence we derive the constitutive relations of the boundary theory in the presence of a magnetic field. This allows us to obtain novel results for the low-frequency magnetothermoelectric response coefficients. We discuss the DC limit of our hydrodynamics in detail, and show that our approach is equivalent to the 'horizon-fluid' of Donos and
... ' of Donos and Gauntlett. Here F µν is the field strength of an external gauge field that we use to turn on a magnetic field, B. Using the fluid/gravity correspondence we evaluate the constitutive relations to O(ε 2 ) in our derivative expansion and the Ward identity to O(ε 4 ). Once again we find that whilst the results agree with  at leading order, there are subleading corrections that need to be taken into account. Given the initial motivation of  with relation to the Nernst effect, it is particularly important to understand how these corrections effect the magnetotransport of the boundary theory. By linearising our constitutive relations in the fluid velocity, v i , we are able to calculate new results for the entire set of low-frequency thermoelectric response coefficients. Of special interest is the ω → 0 limit of these results. It has long been known that this limit is very special within holographic models -in particular it is possible to obtain exact expressions for the DC response coefficients in terms of horizon data [25,    . We therefore end this paper by reformulating our constitutive relations in a new hydrodynamical frame in order to make the structure behind these DC formulae self-evident. In the DC limit, this approach is found to be equivalent to the exact 'horizon-fluid' recently proposed by Donos and Gauntlett [34, 35] . The remainder of this paper is organised as follows. In section 2 we use the fluid/gravity correspondence to construct the constitutive relations of magnetohydrodynamics dual to our holographic model. Since much of the discussion is equivalent to that of , we will be schematic in our presentation of the details. In section 3 we study the linear response of the boundary theory and extract the thermoelectric response coefficients. Finally in section 4 we focus on the DC limit and examine the connection with [34, 35] .