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Simple holographic model of nonlinear conductivity

Accepted version
Peer-reviewed

Type

Article

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Authors

Horowitz, GT 
Iqbal, N 
Santos, JE 

Abstract

We present a simple analytic gravitational solution which describes the holographic dual of a 2+1-dimensional conductor which goes beyond the usual linear response. In particular it includes Joule heating. We find that the nonlinear frequency-dependent conductivity is a constant. Surprisingly, the pressure remains isotropic. We also apply an electric field to a holographic insulator and show that there is a maximum electric field below which it can remain an insulator. Above this critical value, we argue that it becomes a conductor due to pair creation of charged particles. Finally, we study 1+1 and 3+1 dimensional conductors at the nonlinear level; here exact solutions are not available and a perturbative analysis shows that the current becomes time dependent, but in a way that is captured by a time-dependent effective temperature.

Description

Keywords

hep-th, hep-th, gr-qc

Journal Title

Physical Review D - Particles, Fields, Gravitation and Cosmology

Conference Name

Journal ISSN

1550-7998
1550-2368

Volume Title

88

Publisher

American Physical Society (APS)