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2017

Holographic DC conductivity and Onsager relations

Donos, Aristomenis, Gauntlett, Jerome P., Griffin, Tom et al.

Understand

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.