Geometrisation of Ohm's reciprocity relation in a holographic plasma

Abstract

It has been recently pointed out that the familiar reciprocity relation between the conductivity $\sigma$ and resistivity $\rho$, which I refer to as $\text{Ohm’s reciprocity relation}$, should not be expected to hold in all possible settings, but is rather a property that may (or may not) emerge as a consequence of specific features, or in certain limits of interest, of a given theory. In this work I prove an analogous statement: $\rho ={\sigma }^{-1}$, across two different classes of holographic theories related by a generalisation of the electric-magnetic duality in the $D=4+1$ bulk. In terms of the dual hydrodynamic theories, this statement is shown to imply the suppression of any contributions to the transport coefficients from dynamical electromagnetic fields, present in only one of the two theories. This makes the two theories, as far as late-time linear electric transport is concerned, equivalent. I then confirm these findings by considering one specific model and run numerical simulations in different settings.

v2: 20 pages, 5 figures. Major clarification of the main results. Matching published version in JHEP

References in corpus (8)

• Building an AdS/CFT superconductor
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Quantum critical transport, duality, and M-theory
• Hall conductivity from dyonic black holes
• Coherent/incoherent metal transition in a holographic model
• Holographic Axion Model: a simple gravitational tool for quantum matter
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT

Cited by in corpus (1)

• Effective field theories of dissipative fluids with one-form symmetries