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Holographic DC conductivity and Onsager relations

Donos, Aristomenis; Gauntlett, Jerome P.; Griffin, Tom; Lohitsiri, Nakarin; Melgar, Luis

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Jerome P. Gauntlett

Tom Griffin

Nakarin Lohitsiri

Luis Melgar


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.


Donos, A., Gauntlett, J. P., Griffin, T., Lohitsiri, N., & Melgar, L. (2017). Holographic DC conductivity and Onsager relations. Journal of High Energy Physics, 2017(7), Article 6.

Journal Article Type Article
Acceptance Date Jun 24, 2017
Online Publication Date Jul 3, 2017
Publication Date Jul 3, 2017
Deposit Date Jul 25, 2017
Publicly Available Date Jul 25, 2017
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2017
Issue 7
Article Number 6


Published Journal Article (446 Kb)

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Copyright Statement
This article is distributed under the terms of the Creative Commons<br /> Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in<br /> any medium, provided the original author(s) and source are credited.

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