Holographic DC conductivity and Onsager relations

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 $\vartheta F\wedge F$ term in the Lagrangian, where $\vartheta$ 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.

28 pages. Small changes, references and acknowledgement added. Published version

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• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Holographic quantum matter
• Ohm's Law at strong coupling: S duality and the cyclotron resonance
• Quantum Critical Transport and the Hall Angle
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Commensurate lock-in in holographic non-homogeneous lattices
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• DC Conductivity and Higher Derivative Gravity
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