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Holographic DC conductivity and Onsager relations.

Donos, Aristomenis and Gauntlett, Jerome P. and Griffin, Tom and Lohitsiri, Nakarin and Melgar, Luis (2017) 'Holographic DC conductivity and Onsager relations.', Journal of high energy physics., 2017 (7). 006.


Within holography the DC conductivity can be obtained by solving a system of Stokes equations for an auxiliary fluid living on the black hole horizon. We show that these equations can be derived from a novel variational principle involving a functional that depends on the fluid variables of interest as well as the time reversed quantities. This leads to simple derivation of the Onsager relations for the conductivity. We also obtain the relevant Stokes equations for bulk theories of gravity in four dimensions including a ϑF ∧ F term in the Lagrangian, where ϑ is a function of dynamical scalar fields. We discuss various realisations of the anomalous Hall conductivity that this term induces and also solve the Stokes equations for holographic lattices which break translations in one spatial dimension.

Item Type:Article
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Publisher statement:This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:24 June 2017
Date deposited:25 July 2017
Date of first online publication:03 July 2017
Date first made open access:No date available

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