Holographic DC conductivity and Onsager relations

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

Abstract

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.

Citation

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. https://doi.org/10.1007/jhep07%282017%29006

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2017
• Issue: 7
• Article Number: 6
• DOI: https://doi.org/10.1007/jhep07%282017%29006
• Public URL: https://durham-repository.worktribe.com/output/1354072